
Kodak is a Better Film
Also bear in mind that if you were using a disposable camera, you will never get really good pictures just by the sheer nature of a disposable camera. So if you were using a disposable camera AND it has Kodak film in it, that's a double whammy.
When both 35mm still films are processed in their respective chemicals though, I do prefer the look of Kodak film. However I commonly find the look of Fuji motion picture film to be more pleasing, as Kodak film has too much green in it most of the time. The Fuji motion picture film also has better contrast and richer colors in general.
Another cause of "not vividly colorful" pictures may be underexposure. With a single use camera, it is important to not exceed the range of the flash, or to try to use it when there is not enough light for "daylight" exposures. Classic signs of an underexposed negative are "milky" blacks, desaturated colors, and increased graininess.
Kodak has lots of on-line help and tips for taking good pictures:
http://www.kodak.com/US/en/nav/takingPics.shtml
http://www.kodak.com/global/en/consumer/pictureTaking/index.shtml
Here is Kodak information about processing consumer color negative films:
http://www.kodak.com/global/en/service/chemicals/photoChems.jhtml
My favorite film of late is Kodak MAX Zoom (800) film -- lots of versatility and very low grain for such a high speed film:
http://www.kodak.com/global/en/consumer/film/ex_max.shtml#Max800
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John P. Pytlak, Senior Technical Specialist
Worldwide Technical Services, Entertainment Imaging
Research Labs, Building 69, Room 7525A
Rochester, New York, 14650-1922 USA
Tel: +1 585 477 5325 Cell: +1 585 781 4036 Fax: +1 585 722 7243
e-mail: john.pytlak@kodak.com
Web site: http://www.kodak.com/go/motion
Most cinematographers feel that Fuji negative film has more "green" bias than Kodak film. IMHO, reds tend to go more orange also.
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John P. Pytlak, Senior Technical Specialist
Worldwide Technical Services, Entertainment Imaging
Research Labs, Building 69, Room 7525A
Rochester, New York, 14650-1922 USA
Tel: +1 585 477 5325 Cell: +1 585 781 4036 Fax: +1 585 722 7243
e-mail: john.pytlak@kodak.com
Web site: http://www.kodak.com/go/motion
(Please edit your posts when you post back to back instead of replying again.)
As for Fuji cinema film stock (both camera neg and release print), the French use it a great deal and I agree with Mike, blues and greens tend to be more vivid than with Eastman stocks, which appear more vibrant in the red/yellow range. They have two distinct looks, which work well in different kinds of film. IMHO Fuji gives a wonderful look to films where location shooting is more important, whereas Eastman is better in studio lighting.
If you're taking your film to WAL*MART for processing, you shouldn't necessarily expect very good quality from any camera, whether it be Kodak, Fuji or disposable.
Wallyworld has a photo lab installed in their stores for one reason and one reason only: TO KEEP YOU THERE FOR AN HOUR (and find other stuff to buy). They are not supposed to re-do a print that doesn't come out well, as long as there's an image, they'll sell it to you.
I have printed from (and often use) the Kodak and Fuji disposable cameras, and when using the proper corrections, get fine prints (and most people are hard-pressed to tell they're from a disposable). Of course, negatives produced from high-end SLR's produce superior prints...
The kind of chemistry may be important, but from my experience, a commercial labs C-41 could be Kodak, Fuji, Konica or Agfa, and give roughly equivalent results. The REAL difference is the person who is printing from your negative. You need to find someone who can recognize good color, know how to print good color, and most of all, CARE that you get good color.
I have reprinted negatives for people who got lousy work at these discount chain stores (and drugstores) and they were amazed at the difference achieved from the same negative. And, on one occasion, I have brought in my bottle of Filmguard to remove scratches from negatives with absolutely FLAWLESS results.
Just as color timers are important to producing good color in motion pictures, a good printer is essential for your own work. Check out the specialty photography stores in your area, and give them a chance. You'll pay more, but may find that the proper results are worth the extra expense.
Hillary
That about says it all. Taking your pictures to any one hour photo place in a department store or drug store is a huge crap shoot. I think that it's worth going to a more professional photo lab to have the film processed and printed. Sure the goofballs at "Wallyworld" (I love that) know how to make the machine go, but they don't know how to look for problems in their chemistry or a negative. I have found that most professional photo finishers take a little extra time to make sure your negatives and prints come out looking good, and I think that is worth the bit of extra cost.
Fuji and Kodak both make good film. Kodak is a bit more pricy and perhaps a bit better all around. Fuji works fine though. You can often find it cheap, and I think it really does a great job with the bluer end of the spectrum.
In other words, I agree with many of the other posters in saying that rather than pointing the finger at Fuji, you should point more in the general directions of Walmart and the world of the one-time use camera.
As to Brad Millers comments, that one should not expect much from disposable cameras, I am afraid I will have to respectfully differ.
I once felt the same way towards this cheap paper cameras as Brad but I had an opportunity to photograph a snow scene at a resort about 80 miles east of New York City and it turned out to be good enough to be exhibited in the Masters Exhibit at the Professional Photographers of America's annual convention in Orlando Florida a few years ago. For those of you who would like to see this image, please go to my web site at http://www.claudesphoto.com and go to page two at the "IMAGE GALLERY" page and it is there.
Regarding an outstanding motion picture in Fuji Color, one of my favorite is "16 DAYS OF GLORY" about the 1984 Olympics at Los Angeles. Because Fuji was the official film sponsor at these games, all of the official still and motion pictures had to be photographed with their film. I have the movie on a laserdisc but I hope it will be available on DVD someday because the photographic image is just gorgeous.
-Claude
Bottom line: they were taken in on Saturday, the B team ran them & wrecked them. Camera shop developers can't be trusted implicitly.
If it's quicky rip who cares stuff like camera tests, I'll drop them by the 1 hour at Wal-Mart. (Boycott big chain drug stores, they are documented as the number one buyer & demolisher of viable historic structures!)
K-Mart's photo service is advertised as being sent to some Kodak lab; it's one day, not one-hour. Generally it's good, but the processing must have some automated analysis & adjustment of printing to try to make bad photos better. Typically, it will "push" dark photos. That's fine if you've taken a bad one, but if you've got something off the usual curve that's supposed to be dark, it will be wrecked. An example is a photo I took of some the sun behind some stained glass french doors in a theater, with dark, ignored people in front, & the processing decided that I was actually trying to shoot the people, pushed it, & blew out the windows.
But generally, I take them to K-Mart for the convenience & if-it's-not-too-strange quality of some Kodak-badged lab processing.

Kodak's processing manuals specify the washing requirements:
http://www.kodak.com/US/en/motion/support/processing/h243/h2403ulm00041.shtml
http://www.kodak.com/US/en/motion/support/processing/operating7.shtml#final
http://www.kodak.com/US/en/motion/support/processing/operating6.shtml#wash-water
http://www.kodak.com/US/en/motion/support/processing/h249/h2409_03.shtml#162744
http://www.kodak.com/US/en/motion/support/processing/h249/h2409_03.shtml#162993
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John P. Pytlak, Senior Technical Specialist
Worldwide Technical Services, Entertainment Imaging
Research Labs, Building 69, Room 7525A
Rochester, New York, 14650-1922 USA
Tel: +1 585 477 5325 Cell: +1 585 781 4036 Fax: +1 585 722 7243
e-mail: john.pytlak@kodak.com
Web site: http://www.kodak.com/go/motion
-Claude
Several years ago, a manager at a particular lab told me they don't mix the stabilizer in the water for the final wash. When I asked them why not, the answer was that it puts spots on the film. This was the solution, rather than finding a way to avoid the spots, and help prevent dye loss. Such concern for the customers' precious images is heartwarming 
The lab where I work (which is part of a chain of specialty stores) has gained a reputation in the area for superior work, but after having seen work from the other labs in our district, I totally agree with William that you cannot trust a Camera shop lab implicitly. The training offered by our company is adequate, but so few people care anymore, it's maddening, and often the quality is equivalent to the discount chain stores. The best way is to start with a lab which caters to professionals, or do some tests with short rolls or reprints.