I'd say Vesta as well. Good PvE Boat. Like all Science ships, she's a little light on hull. However the advantages gained outweigh this disadvantage by a fair amount. I've never used the MVAE, so I cannot speak specifically about this ship. But my toons seem to hold their own against most Escorts in PvP and I do pretty well in things like Azure Nebula and Starbase 24 as well.
I will suggest a few other things for you to think about before making your choice.
1) A good Captain makes a good ship, not the other way around.
2) Regardless of your choice, focus on having fun with it.
The enjoyment you get from playing STO the way you want to is the only true Optional and the one you should try for every time you start up the game.
How is the Vesta more work than the MVAE? I've heard it has a lot of weird builds, and one individual claimed you'd have to respec a few times to get the most out of the Vesta. (Probably meant that you'd have to experiment, I'd guess)
The MVAE can get excellent performance with very straightforward and frequently discussed builds, and it's much more agile which makes it easier to keep the DHCs on target. A Vesta build is a complicated balancing act between all the different things you want to do, and because no one comes down in the same place on that there isn't really a go to basic setup to use.
Thanks for the input, everyone. Looks like I'll be saving up for the Vesta afterall. Admittedly I'm not too fussed, as I've never really been a fan of the MVAE's aesthetic. The Vesta doesn't look too bad, and it'd certainly feel more "at home" on my science captain.
I fly the AE and the Vesta Tactical (have the pack though) with my Fed Eng.
I know that the AE is a little different from the MVAE, great escort, great fire power with a bit of a Sci leaning but the Vesta feels like an escort... just more powerful. I like using the QFFP on Cubes and gates, very significant DPS burst against big unshielded targets.
I don't see that attraction of the MVAE's consoles, it's a nice gadget with mediocre AI. The Vesta consoles can be very useful for taking out targets and supporting allied ships.
The Vesta may have lower hull than cruisers and some escorts but it still does VERY well. I have died very few times only because I wasn't paying attention. It has a lot of firepower and great on Science power as well.
I think that adding SIF Generators would be a good idea to take advantage of the Aux being cranked-up. Also I did not notice significant drain from the Aux cannons to be of concern - so again, crank up the Aux power to the Max. You'd want to add an Overcharged warp core for the additional Aux power.
The Excelsior has been my main ship and the Vesta is a close second, probably just because the Excelsior has the Transwarp computer and I like tanking once in a while as well. The Vesta might give me a good reason to respec to have better GW/Science abilities.
Those are my scattered thoughts, hope some of it made sense.
The primary reason for the MVAE was the LT. Cmdr Science Bridge Officer. You lose out on some tactical slots, but gain the ability to toss out a Gravity Well I or something else. So you're still primarily focused on DPS, but also have more utility than the average escort. The actual console is a novelty, indeed.
However, the Vesta just seems to be better, with the myriad of options it has available.