The Tele body is slightly thinner, and if you phone or e-mail in your order (or wait for one to come up in the showcase) then you can get it made completely solid without a laminate top. A thinner body is neither a definitive pro or con, just personal preference. Some people will tell you that not having the laminated top makes for better sustain and clearer bass, though I myself find there are simply too many other variables to attribute such differences solely to the presence of a laminated top)
I've done all three builds you've suggested: an LP-like carved Tele from Warmoth with a conversion neck; a bolt-on LP from Warmoth (before they made the cutout sharper and renamed it to the Regal); and a setneck build from "another company in Canada". None of them have similar electronics, however, and the Tele has an all-rosewood neck instead of mahogany+rosewood like the other two, and I have them set up for different tunings and styles, but acoustically they ring out the same and there aren't any differences which I can definitively attribute to the body shape or construction...
... Except the neck pickup on the bolt-ons always has a slightly clearer chime to it. And that goes for every build I've made (a couple dozen at this point) and every guitar I've bought (several dozen more). All-else being equal, bolt-ons always give a bit more of a sparkle or twang to the neck pickup compared to setnecks or neck-through instruments. I've found that the difference can be compensated for with a change in pickup, pickup magnet(s), or simply lowering or raising the height of the pickup. For example, my most standard setneck LP has a Gibson BurstBucker #2 in the neck position, which is a generic PAF-copy; mid-wound with an A2 magnet. My LP-like Tele has a BurstBucker #3 in the neck, which is the same pickup just slightly overwound, and that resulted in the same tonal balance (but slightly more output) as the BB#2 did in the setneck LP.
My advice for anyone making any build is simple. Tone can be changed in a million different ways, and even if you've had a hundred guitars, you can still never be 100% sure how a guitar will sound until it's fully finished and plugged in. So don't worry about the tone. Buy the guitar (or in this case, parts) which feel and look best to you, since the feel and the look are the two aspects which either can't be changed or are very hard/expensive to change. Figure out the tone later.