Having owned both the TX200 Mk3 rifle, anda Pro Sport, both in walnut and both .177, albeit at different points in time so never truly did a back to back test, what I will say is this:
The weight balance on the TX200 Mk3 rifle (full length) was very far forward and felt like a right old lump when shooting offhand. The shot cycle was incredibly smooth and the mass of the rifle absorbed most of the recoil.
The weight of the Pro Sport is definitely more rearward and this helps drastically when shooting offhand. I'd argue that there was more felt recoil from the Pro Sport.
Ergonomically the TX is probably easier to live with despite the ABT. As others have said the ABT becomes second nature, whereas the awkward arc that the recessed cocking lever moves in on the Pro Sport can make make usage feel like a bit of a faff.
Both guns had smooth shot cycles, I'd argue that MY Pro Sport wasn't as smooth to shoot as my TX, but that could just be due to manufacturing variation.
I'm also curious as to whether the HC variant of the TX is the sweet spot between the two with regards to balance, but have never had the chance to handle one.
If I was to pursue purchasing another springer, it would definitely be one of the Air Arms range as I feel fit and finish and general build quality out of the box far surpasses any of their rivals (the Weihrauch stuff is good don't get me wrong, but I feel that the finish is less refined and the stockwork looks slightly agricultural by comparison).
If I was buying with my head, I'd have another TX as it's easier to handle in the field due to more ergonomic cocking cycle, but if I was buying eith my heart it would have to be the Pro Sport - I don't think there's a better looking air rifle out there. Out of the two, I regret selling my Pro Sport the most.
Best of luck with whatever you choose to purchase. If you feel like you've made the wrong purchase I'll gladly take it off your hands
ATB
Ash