Since Daniel beat me to the list, I'll tackle the "let's go through and see why people don't swap them" (or maybe "why they should" - I'm writing this before doing the lookup.
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Queen's Borg Sphere (First Contact) and Queen's Borg Sphere (Resistance is Futile)
The RIF version is +1 WEAPONS, +1 RANGE (and FC is RANGE 5, so every point counts!), adds Borg Queen as an optional staffing requirement, and swaps the niche Temporal Vortex download for the much nicer Optimize Drones. I suspect if the downloads were switched you might see people grab the Optimize download and then swap to the better stats (and second possible download), but in general I'd say this is just a Strictly Better problem, combined with "spheres kinda suck and no-one uses them anyway" (according to the deckbuilder)
U.S.S. Enterprise-E (20th Anniversary), U.S.S. Enterprise-E (Chain of Command), and U.S.S. Enterprise-E (First Contact)
One is Borg, so swapping is off the table. Between the other two, CoC seems to be the deckbuilding favorite (probably because once you staff it you've matched the FC's stats, and then you get to pile on the bonus generally as opposed to FC's flat bonus against Borg stuff. No downloads, and not really even a situational bonus. So if you're allowed the CoC version I can't see why you wouldn't use it.
Starship Enterprise (Chain of Command), Starship Enterprise (The Trouble with Tribbles), and Starship Enterprise (The Motion Pictures)
Weirdly, the one that gives you a download of *any* OS personnel (the TwT version) is by far the most popular. Who woulda thunk?
CoC swaps the download for
Where No Man Has Gone Before (which is good but not "any personnel" good), and TMP staffs on Movie rather than OS, so that's a hard ask to swap between.
If there was a fast way to swap between CoC and TwT, I could see people thinking of double-dipping maybe. But it's another "why not use the good version" issue.
Stolen Defiant, U.S.S. Defiant (Chain of Command), and U.S.S. Defiant (Deep Space 9)
Stolen Defiant is
(incl. in the staffing), so not a lot of desire to swap in/out of that. Between the other two, you're choosing between +1 SHIELDS or +3 WEAPONS & SHIELDS vs [Borg], and the deckbuilder stats seem pretty clear that folks will take the guaranteed point of SHIELDS over the situational bump. (And are you going to stock CoC Defiant just in case you face a Borg opponent, when the bonus doesn't really make the math better?)
U.S.S. Enterprise (Premiere), U.S.S. Enterprise (Chain of Command), and U.S.S. Enterprise (20th Anniversary)
Setting aside the Ferengi version, the deckbuilder suggests this is a pretty even matchup and I'm not sure why - the CoC version downloads Wall of Ships which gets you either another Enterprise or a stat bump that makes up for the lower specs. So either people actually are playing both (swapping to Premiere to up the stats after firing the download), or - and this is my guess - the deckbuilder stats are skewing to all those OTSD/Premiere events
U.S.S. Voyager (Voyager), U.S.S. Voyager (Chain of Command), and Voyager (Engage)
This is an interesting one - each ship hits a different niche (Kazon, DQ Fed, Alpha Fed), that I think swapping probably isn't a great idea for any of them. Maybe my favorite set of personae so far.
Cha'Joh (The Sky's the Limit) and Cha'Joh (Deep Space 9)
One gets double commanders and Romulans, one reports to Soran. I saw someone mention that they wanted to try this one, and now I'm really curious why, because I'm not seeing the upside for the Soran version.
I.K.C. Pagh (Premiere) and I.K.S. Pagh (The Next Generation)
Another one where I wonder if Premiere is inflating the numbers. TNG version loses a point of RANGE and gains "draw an extra tactic". I suppose mileage may vary on which is better, but you probably don't want to swap.
Liberty (Voyager) and Val Jean (The Maquis)
Unsurprisingly, Liberty gets more use here - better stats, can play in DQ, reporting ability. Val Jean is much more niche.
So, in summary: why don't people swap ships?
* A lot of ships are niche plays - different affiliation, different faction, different staffing icons - so you couldn't easily play either
* Most ships don't have abilities that are worth swapping into/out of. The reason Borg Queen sees swaps is that those two downloads are great, and then you get the skill beast.
* It's not worth the hassle to stock extra copies and then find them. The other reason Borg Queen sees swaps is that she's a good probe and Borg download like freaks so there's no downside in having a ton of copies.
Not sure what the lesson is, but hey - research!