Most kids are still watching the Spider-Man movies religiously. They're not going to care about a reboot, because Raimi's movies are still fresh in people's minds and are very much a part of pop culture. It's been 8 years since the first Spider-Man came out.
When Batman Begins came out, it was 16 years after the original, and it was following an absolutely abysmal fourth installment. There was NO GOING BACK from Batman and Robin. The franchise's dignity had been permanently damaged, and the only way to escape Joel's Schumuckery was to reboot.
Spider-Man, for all the fans' whining was a well recieved movie and they could have easily released Spider-Man 4 with a solid reception. What did fanboys hate about Spider-Man 3? They screwed up Venom and they had Peter dancing. Boo hoo, let it go and and move on.
Batman rebooted out of necessity. There were no market trends to indicate that reboots would make lots of money, so Warner Bros. was doing it because they wanted to restore the franchise's dignity and a reboot was their only chance. Now, people reboot because it's more fashionable than fixing a franchise with a good sequel. Now if a franchise misses a note, they just hit the reboot button.
The sad part of all this is that we're STILL waiting for a proper Superman reboot, and yet there are tons of movies that SHOULDN'T be rebooted that get rebooted anyway. Reboot-itis is probably the worst thing to happen to movies in the 21st century. It really is a shame, because rebooting CAN be a good way to save a franchise, but like all good tools it inevitably gets abused and used for the wrong job constantly. Franchises that actually need reboots get overlooked, and popular franchises get reboots just because it's easier than coming up with new ways to grow characters.