Ease of breathing I didn't notice any difference, but really almost all of those breathing results require a machine to actually demonstrate a difference. We're generally not perceptible enough to notice unless it's an extreme difference.
I don't know the weight difference, but the MTX-R is big and chunky. By feel it was heavier, but I haven't had one in my hands in probably 8 months. I seem to remember it being a noticeable difference, but Apeks doesn't list the weight online for comparison so I wouldn't be able to give you a definitive answer other than, "I remember it being heavier."
The Tek3 is basically just a DS4 except all the ports are on one side, so physically it is similar in size. The DST is just a DS4 with a turret swivel, so closer in length to the MTX-R. The MTX-R is definitely bigger in physical size than either..
I don't mind the bending of hoses with the Tek3's, I replace all my hoses regularly as I treat them as consumable items. I like that their natural position out of the regulator is down. The natural position of the hoses out of the MTX-R is out. That bugs me, but that's probably more of a personal thing than anything. I'm not sure that it really makes a difference. Personally I think the DST with a 5th port has the best hose routing, if that gives you an idea of my preference.
Really, I think the Tek3's shine on a rebreather. I think the DST's with 5th port are the best for backmounted twins or sidemount. We had some MTX-R's at work and I just didn't really care for them. That being said, we didn't have a need for super cold water performance, so I don't know if that would make a difference.