I'm a big Trek fan in general, and I LIKED the new Star Trek just fine. But it didn't really feel like Star Trek at all, it frankly felt a lot more like Star Wars.
One of the things I always thought was cool about Star Trek in general was that the crews were mostly made up of pretty ordinary people that didn't have super abilities or anything like that. Just people trying to do the best they could in crazy situations. The new Star Trek is totally the opposite of that - everybody is a young super genius who is the best in their class at something or other. It's no longer a bunch of average people who have learned through experience, you know? Chekov is some kind of super math genius, Uhura can hear crazy signals that nobody else can, Kirk is some kind of Luke Skywalker boy of destiny...
I'm not saying it wasn't fun and good, I enjoyed it quite a bit. I even bought the DVD. But as a fan of the old shows and movies, it's really Star Trek in name only and I totally get why old Trek fans don't like it.
It really could have just been "Space Action Movie" instead of having the Star Trek name. And it still would have been fun.
EDIT: Also I think ol' JJ could probably do a pretty good Star Wars movie based on the Star Trek movie he did. The remark about the same director doing Star Trek and Star Wars though is spot on - it's a weird thing to contemplate. :-D