Parkerizing -- essentially the application of a phosphate coating -- has long been the first choice of the military. The advantages of parkerizing are many: it is relatively long wearing, provides good corrosion resistance, requires little in the way of maintenance, and is easy to reapply. It is an excellent choice for "hard use" guns which may not (for whatever reason) receive regular care.
A matte finish refers more to the lack of luster or shine, and not to any specific formulation or application procedure. Parkerized finishes tend to have a flat "matte" appearance, as do many of the newer polymer coatings, such as Black-T or Armor-Tuff. The idea behind a matte finish is less light reflection, hence, greater suitability for tactical applications where stealth is important.
Blued finishes require somewhat more care (though not too much), are a bit easier to wear off of edges, and usually exhibit a deep, glossy appearance. They are more than up to the task however, and most folks tend to view them as the most appealing in a visual sense.
Which finish is right for you really depends upon what you plan to do with the pistol, what sort of climate you live in, and how often you are able to clean it. For what I would call a "normal" shooter, a blued gun is probably about as close to perfection as you will ever need to get. Those who carry on a daily basis or in adverse climates may have more stringent requirements, and opt for finishes with greater durability and corrosion resistance, such as hard chrome or parkerization.
I'm especially pleased with the park finish on my new Repro Colt. Very salty looking and TOUGH! It is starting to wear just a little on some of the sharp edges. I'm also surprised by the smoothness. Colt has been pretty famous (here lately) for really rough bead blasting. Some of the 1991A1s I've handled looked like they'd been 'blasted by something from Fred Flintstone's quarry. The rounds on my Pocket Nine are an example of that.
Anyhoo, the Repro is SMOOTH with just enough 'matte' to diffuse light reflection and hold onto Breakfree CLP for long periods. I recently recieved a Wilson Bulletproof extractor (the factory extractor in my Repro was Series 80 and BLUED, it just didn't "do it" for me) and the park finish was AWESOME. Totally matched the gun like it was MADE for it.
Parko is also a mil-spec prerequisite for some things that are to be painted, since it makes such a "thirsty" base for the paint to lock into. For that reason, I feel that the only time one of the fancy-schmantzy polymer bake-on finishes is at its optimum is when it's applied over new Parkerizing.