I am a screen printer in real life. It is what I know, it is what I do. I see so many people on eBay getting ripped off because some kid at home is printing iron ons and selling them as something else. Basically there are a few levels of quality clothing.
Low Quality: Iron on - Made at home with plastic paper and any inkjet printer, peels off and discolors within 1-2 washes. Poor quality.
*new* DTG(DIRECT TO GARMENT) - this is a modified ink jet printer that prints digital images direct to shirt like a printer. This technology sounds good in theory, but unfortunately the quality leaves much to be desired. The image will appear dull in color, splotchy and blurry. May "bleed" and discolor even before the first wash.
Medium Quality: Sublimation Heat transfer - Printed on a high DPI printer, applied with a commercial heat press at very high temp. Lasts years, fades slightly, usually needs to be on 100% polyester and white or light colored garments.
High Quality: Screenprint - Printed on a screen printing press, color by color, with a plastic based ink. Ben Franklin was a screen printer, and actually used leaves from trees, as a security measure. High in detail, crooks would be less likely to recreate bills with such high details. This is the kind of quality that you see in retail stores everywhere. The printed designs are even higher in clarity now days due to high DPI image editing software, and high DPI printers able to hold fine details on the film. For photo like prints, we use screens are 300 DPI(300 "mesh count"). The normal computer monitor is only 72 DPI. Some prints feel plastic like when they have a thick layer of ink. Others feel thin, and some even have no hand at all. The last, is usually a water based ink with color pigments mixed to specification. Many printers don't like printing water based inks due to the extra mess and time incurred. Screen printing lasts years, doesn't fade if properly printed, small cracks may appear over time but overall the image will remain and outlast the fiber material. Now days the cracked or artificially aged("distressed") image can be in more demand than that of a newly printed, crisp look.
If you want to be disappointed, go with the Iron on. You will be kicking yourself in the butt shortly after getting your item. You can tell if you have an iron on if the edges of the image appear to be different than the image APPLIED to the shirt. Usually people applying such low quality prints don't take the time to properly trim the extra around the edges. This will look like white or clear usually.
If you get a heat transfer you'll be in better shape. Though not the quality of an actual screen print, heat transfers(if applied commercially, not just saying they did) will actually form a gas when its being applied. This gas seals the transfer to the fibers of the shirt making a much better, longer lasting image.
Screenprint is the way you want to go. They last a very long time due to the fact the ink used, is plastic based, and adheres permanently to the fibers of the fabric. A properly screen printed design will last longer than the garment itself.