I have the Canvas Stretcher and love it. In practice either one is excellent. I bought the CS because it doesn't take up as much room as the Tensador. I just saw John, owner and inventor, at the WCAF show and he is able to do the stapling from the front side. But everyone else I know seems to walk around to the back side to do canvas stapling. If you need to do that then while you are using it you need to get to the back side taking up some space, which I didn't have.
As to tension I wondered the same thing and when I was at WCAF tested the tension by thumping on a couple of canvases that John and Randy Hufford had on display. Couldn't tell any difference between what they had and what I get with the CS. May also be a function of whether you have a 100% cotton canvas (I use Hahnemuhle Monet) or one of the more common cotton/poly blends. I would make an assumption that the cotton/poly has slightly less stretch and tighter tension.
I had one question on the size of the push plates and CS immediately sent me some that were more adjustable.
I like being able to lay the artwork on my work table and do all of the work right there. If you watch Andrew Collette in the LLJ19 video you see him layout on his work table, and then go back and forth to his Tensador. WIth the CS you stay in one place.
I know that Dan Berg who posts here and does a bunch of work also has one and maybe he will chime in.
Gary