I played an Engineer Escort in beta till about Commander 5, I'm now playing a Tactical Escort and am Lt. Cmd 3. I have to say Tactical Escorts are much better so far. Escorts are all about quickly eliminating one or two targets very quickly to ensure victory. I've handled a lot more being a Tactical Captain than I could with my Engineer. Of course any combination is still viable, but I do have to believe some are better than others depending what your role is. I really did love being an Engineering Captain with both Science and Cruisers though. I haven't tried a Science Captain yet, it's on my to do list :p
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I'm going engineer and science. I usualy play tanks and healers. These come close to those classes. Support claases are always in demand. DPS is usualy the most common as many players love to blast everything in sight.
Based on my very limited experience, I found Engineer uber effective for soloing. Put together a BO team of two engineers, one tactical and one science (along with your guy). Watch as no NPC can really hurt anyone hiding behind your shield generators and shield buffs. Even AOE attacks, which can hit everyone huddled together and wreck equipment, are just little annoyances because you're throwing up new field works every few seconds as are, quite possibly, your other engineer BOs.
In space, Engineers make every ship more survivable and they make the ubersturdy cruisers even tougher.
That said, I'm going Tactical this time. I just like being out and maneuvering for flanking shots or to get into melee range more interesting than hunkering down inside a shield generator radius with my BOs.
Haven't tried Science at all yet so no opinion there.
In Beta I played an Engineer who used turrets. I thought it was pretty nice and quite powerful.
In Space, the engineer abilities are very effective and very straightforward; an engineer in a cruiser who uses repair shield/hull buffs is extremely difficult to kill.
On the ground, well, turrets are very powerful. Setting them up was kind of annoying though. I note, however, that turrets draw fire - this can be a good thing! Even a phaser turret could be seen as a defensive structure on account of this. Frankly, I think phaser turrets are the best turret, followed by shield turret (medical is ok, but not really strong enough to make a difference when you need it and quantum mortars are too slow and can miss). It's like having extra bridge officers, in terms of firepower. I also tried chroniton mines, which I liked, and transphasic bombs, which I didn't really like and found them to be too weak to really make a huge difference.
That being said, I have now gone Tactical - but am still using a cruiser and primarily engineer BO's. Here's why: as I mentioned, turrets are too annoying to place for ground combat (for me - my BO's will use phaser turrets I and II, and probably a drone for last place). I would rather have the ability to use the mostly instant and very effective tactical officer powers for my own character - especially since I do like the option to melee - than worry about placing turrets myself. My BO's will be all engineer except one, which will be the usual science officer with heals (and the +physical damage buff, that's pretty nice). I get to charge into combat supported by healing, multiple shield regens, +phys damage and a bunch of laser turrets. Yeah, I like that.
In Space, it's almost an even trade. Almost. The tactical powers are really quite nice, and Attack Pattern Alpha gives you a second way to improve on the abyssmal turning rate of a cruiser, and it lasts for 30 seconds too (the damage buff's nice too, of course). I'm not sure it's really less survivability when you can kill your enemies - and change shield facing - this much faster as a result. I think I prefer tactical space powers to engineering ones, although I reserve the right to change my mind after I've been able to see things all the way to Admiral.
Overall, had I not wanted the option to melee, I might have stayed engineer, but I really do think this is a bit better overall... if you care about ground actions, which I do. In terms of Space, it's an even trade, or so it seems.