Clipless allows your feet to "clip" into a pedal--theoretically this allows you to bring more power and efficiency to your stroke, particularly if you're climbing hills. However, it also requires you to have special shoes, most of which are terrible for walking in once you get off the bike. There's also a learning curve that leads to a lot of people falling down as they get used to have their feet secured to the pedal.

Platform pedals let you use any shoe you want, but some riders don't like that your feet can come off the pedal if they're going too fast. Also, in rainy conditions some people complain about their feet slipping.

I commuted for a year using clipless, but started using platform pedals (Grip Kings--highly recommend them!) about a year ago. Personally, I think good grippy platforms are fine for the 99% of us who aren't racers, and the advantage of being able to jump on the bike wearing shoes/sandals/boots is a huge plus. I feel like I'm just about as fast on platforms as with clipless and can keep up with my old man on his carbon fiber wunderbike just fine.