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Setting aside the issue of the Vesta, which may or may not break everything (I'm not jumping on that gravy train):
Wells TSV has:
1.45 shield modifier
15 turn rate
3 tac, 3 eng, 4 sci consoles
+15 Aux power
Lt. Cmdr Uni
Tholian Orb Weaver has:
1.4 shield modifier
3 tac, 3 eng, 4 sci consoles
+15 Aux power
Tholian Web Generator
Lt. Cmdr. Uni
Lt. Cmdr. Eng.
In a way, I think the Wells is a great deal more versatile. They share the same bonus to Aux and the same console layout, but the Wells has a much higher turn rate and slightly higher shield modifier. I would also say that the Wells console is more beneficial than that of the Orb Weaver; the Wells console is a free hull and shield heal, while the Orb Weaver's console is... of dubious use as far as I can tell.
(Note: I have the Wells, but not the Orb Weaver).
I personally use the Wells with my tactical captain, and use both universal boffs as tactical boffs. With the high turn rate and good tactical boff setup available, this makes the Wells a pretty potent little ship. But of course you don't have to do that, and that's the benefit of the Wells.
Both ships share a science commander slot (obviously, as science ships). So then it all boils down to what else you want to do with it. The Orb Weaver has the potential to be a much better tank- you can slot in two engineering Lt. Cmdrs- while the Wells has the potential to be a much better escort with a Lt. Cmdr Tac and a Lt. Tac plus the higher turn rate.
Both ships would let you slot even more science officers, if you really wanted to go that way. Honestly, it seems to me that the Wells is a more versatile and more adaptable ship (helps with the two universal slots). The only situation in which I'd choose the Wells, I think, is if you wanted to go heavily into a science/tank build, and basically slotted another Engineering boff. That would be potent. But if you want to go tactical/science, I'd go with the Wells.
Having played both, the Wells outclasses the weaver in all aspects. My playing style leans more to an escort and the wells answers well with excellent mobility. The Aux bonus plays well, and the added effect of essentially a 'heal everything' console is great. Note: don't have your butt pointed at anything when you use the Tipler console - I have found myself inside cubes and portals with no way to get out.
I have added the Manheim console from the destroyer variant, making for a decent attack spike for 30 seconds.
1.35 shield modifier
Six consoles (either 3, 2, 5 for the sci version, 4, 2, 4 for the tac version, or 3, 3, 4 for the eng version)
At least +10 to aux (+15 sci, +5 weps tac, +5 shields eng)
Lt. Cmdr. Uni
1. Hangar bay
And of course the various console powers:
Sci: self and ally hull/shield repair and buff to particle generators
Tac: Spinal lance weapon
Eng: immunity to hold, repel close targets, reflect kinetic damage
So you've got a weaker hull and shields than both other ships, but with a turn that's slower than the wells and faster than the Orb Weaver.
On top of that, you have a boff layout that leads itself to specific tradeoffs; sometimes beneficial, sometimes not. For example, if you want to go tank you can put a Lt. Cmdr. Eng. into that universal slot and have a Lt./Lt. Cmdr pair, but that leaves you with ****ty tactical options (Lt. and Ens. at best; only a Lt. if you use that Ens. for Sci.) On the other hand, if you want to go tactical, you can slot a Lt. Cmdr Tac, which gives you the Lt./Lt.Cmdr pairing there. With the Ens. universal in engineering, you get a very balanced ship.
One of the issues here is the weapon. The Vesta can mount cannons, and in fact comes with a Mk XII dual heavy phaser cannon. Now, that phaser drains Aux instead of Weapons power. But you have two issues with this: First, you lose subsystem targeting. Second, this seems to leave you in a tight spot. You have a 3/3 weapons layout, and you could (I presume) run three Mk XII DHC [Aux] cannons forward with all power in Aux, but that seems to leave you without subsystem targeting on one hand and with ****ty options for aft weapons (unless you went all torpedoes aft, I suppose).
In a way, I see the Vesta as a more balanced ship than either the Wells or the Orb Weaver (which seem to lend themselves to Tac/Sci and Eng/Sci, respectively), but one that would require careful planning to get the best out of.
The hangar bay is of course the other wild card, and it gives the Vesta options neither other science ship has.
Now... the truth is I imagine trying to run the Vesta as an Armitage with SCIENCE is going to put its owner into a world of hurt, despite the fact that superficially the ships are much the same. I'm not even sure, if I had the Vesta, that I'd slot the dual cannons at all.
It's very simple. The devs said each new lock box ship will be better than the last. And the Wells compared to the Orb Weaver is no exception. Wells is a better ship by far. The only thing the Orb Weaver has over the Wells is appearance, and that's only my opinion, not a fact.
It is said the best weapon is one that is never fired. I disagree. The best weapon is one you only have to fire... once.