Does anybody have an opinion on what the differences/similarities between these two rods are?

I have a couple of Sage Ones and one Sage TCX, but in different weights, so it's tough to get an apples to apples comparison. My sense is that the TCX is a slightly faster rod with more backbone. It can probably handle slightly larger flies.

The Sage One is lighter and shoots line a bit better. I'm guessing in similar line weights it would also be slightly more responsive and less likely to cause fatigue after a long day of casting.

Both are at the very fast end of the spectrum, so you can expect tight loops and long casts (in the right hands).

I like stiff rods, but I think the TCX is too stiff. Its a lot more fast than the One. I have cast the TCX, Xi3, One, Bass II and several others. The TCX is not unforgiving, but its less forgiving than the others. The Xi3 is almost as fast, and the One is slower than the Xi3. The One has to be the most forgiving rod that i have ever touched. Its fast but not ultra fast of the Xi3 or the TCX. You will find that the One doesnt shoot as far as the TCX and I personally think it is not as well suited for really heavy flies.

The Sage TCX is really designed for one thing, casting long distances and in heavy wind. This rod will not load properly with the recommended flyline wt. at distances less than about 35'. Now this rod will cast/deliver all the flyline much easier than a ONE fly rod. Some will want to overline this rod with a weight heavier flyline for fishing under normal distances.
The ONE is really still a fast loading rod, but it is designed to load at shorter distances, but even this rod will not properly load at very close distances say 20' or less. But at 20 to 70' this rod performs well.
If you need something that will load at very close distances you need to look at something like the Circa that excels at 10 to 40'.
So the TCX is really a specialty rod used for things like Bonefishing, fishing sinking lines, or other fishing that requires casting great distances.
The ONE is much more an all-round rod really designed to do it all from dryfly fishing, nymph fishing, or even streamer fishing.

Next to the XP, the TCX is my next favorite rod. Its my go-to rod for streamer fishing or Pike fishing. Like everybody else said, its a bit faster than the ONE. As fast as the ONE is, its a heak of a lot easier to load and cast than the TCX. Its capable of throwing heavy flies in wind with the right line, but the TCX is ideal for it. I guess it just comes down to what you want to use the rod for. All around, go with the ONE. Throwin wet socks, go with the TCX!!