Pros of using the Web as a platform:
- Instant accessible distribution channel: You can easily give the URL of your game to anyone to play it.
- Low entry barrier: The tools available are free or available at a low cost, and you don't need a license to develop on the web. Just a server and a domain.
Cons:
Perception of "Cheap" games: the low entry barrier has made that a lot of games out there are not very good or don't look very good, plus they're free. That makes a difficult problem to figure out how to charge for your game.
Performance dependent on client configuration: In contrast to a console, such as an Xbox 360, or a cell phone, there are a lot of configurations of PCs, each one with its own performance. You might find that your game runs well on your special developer machine, but won't run as well on your mother's Pentium Celeron. This is typical of PC development, and you should make sure when developing web games that yours does not hog too much resources.
I recommend you to read the Flash Love Letter (Part 1 and Part 2) which I think they're great articles that speak of web game development.