I haven't played EVE. But I'm in love with Star Trek Online. While the gameplay is certainly nothing new, from what I've heard, it's got the basic things you'd want in a Star Trek game, I think. You get your own ship, the ability to customize that ship, hand-pick and train your own crew, and get to play through what're actually very good story arcs.
Its simplicity is kind of an advantage, I think. You can dive straight in, and you don't feel like you're missing anything because you can't figure out how to do something. The biggest thing to learn is how to navigate the sector maps. There is some strategy involved in the space combat, although you can not even pay attention on the ground missions and do just fine. Positioning is huge in space, and figuring out the right mix of weapons, speed, and shield facing is a lot more complicated than it looks. You have control over the ship's power settings as well, so you can fine tune the ship to exactly what works for you. Finding those settings, however, takes some time.
I don't care for the PvP on STO, though. It's very unbalanced-- the Klingons have a tremendous advantage over Federation players due to the cloaking devices, which have a negligibly short recharge time. The tradeoff is that Klingon players don't have anything to do at the moment except PvP.
If you're a trekkie, it's something you need to at least give a few days to (it starts to shine once you reach Lieutenant Commander rank when you get a Tier 2 ship). If not, it's one of those things you'll either love or hate depending on your taste in game mechanics. From all the comparisons between STO and EVE I've read on the comms channel on STO, EVE is more complicated, but not necessarily better unless you like things that are complicated for the sake of complexity.
One of the things I really like about STO is that if you've got fifteen minutes to kill, and want to just blow stuff up, you can engage wandering enemies on the sector maps. The space combat is a lot of fun, and for some reason, flying through a squadron of enemy ships with phasers firing is immensely satisfying.
There's not really level grinding the way there is on other MMOs, from what I've heard. You level up by playing the missions, so you're progressing through the story steadily as you level. You don't need to go grind through a thousand enemies before taking on the next mission-- you're usually good to go as soon as you get the orders from Starfleet.
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