There is no denying that both are great guitars and that they have been the choice of many guitar legends over the years. They each have their own set of advantages and disadvantages.
With a Fender guitar, you have great tonal flexibility. You can produce sounds ranging from Clapton blues to grungy rock like Nirvana. Fat Strats, with the added humbucker, can make achieving the latter a little easier. You do not need a great amp or tons of effects pedals to get your desired sound from a Fender. Fender guitars are also considerably lighter than Gibson guitars, making them easier for carrying around to gigs.
Gibson guitars are made of sturdier material than Fender guitars. This adds to their weight, and they can be a hassle to carry around. They also tend to be more expensive than Fender guitars. With a Gibson guitar, however, you get a much fuller rock sound that no Strat(even with a humbucker) can quite match. It is a better choice if your focus is on hard rock/metal guitar playing.
Personally, I like Fender guitars. I play a lot of bluesy rock, so the Stratocaster was a perfect fit for me. But at the same time I recognize that there are times when a Gibson would be much more appropriate. Many guitarists own both, and use one or the other depending on the situation.