Normans
This link has some info about trumpet options including tuning slides.
The rounded slide doesn't let more air through, but "feels" more open due to less resistance.
With reverse tuning slide configurations the theory is that you don't have a "bump" the thickness of the tuning slide where your slide is inserted into the lead pipe. Many folks think that this can lead to a freer blowing horn and possibly more responsive. This is tough to determine though because often times in the reversed tuning slide, there will be less bracing (sometimes none). The normal Bach Strad has 1 brace between the lead pipe and the pipe leading into the valve cluster and a brace between the upper and lower portion of the tuning slide. The Strad with a reverse configuration only has the one brace. I you played both there would be a difference, but is it the bracing that effects the sound/feel or the reverse tuning slide?
Essentially you have to play some with different options and see which configuration you like best.
I have a lightweight Yamaha that has reverse tuning slide and no bracing between the lead pipe and lower pipe. This is a very responsive horn due to this configuration.
My Conn Vintage One came with both the traditional "D" shaped tuning slide and a rounded slide. The feel between the 2 slides is very different with all other factors being the same. The rounded one "feels" much more open and responsive. The "D" shaped slide does add more resistance and plays with less effort, but not as responsive.
Almost everything you can do to a trumpet will have a pro and a con. Finding the right balance for you is the key.