There is nothing wrong with owning both, but I feel that the triggers are so radically different between the two, that one is best picking between the two and sticking with it. This might not be evident in casual plinking or paper shooting at the local range, but when you add a shot timer, drawing from concealment, movement, and multiple targets, a familiar trigger becomes something you start to lean on for consistency more and more.
Personally, I feel that the 53 is just as good as the 13, if not better with the slimmer profile, the 13 is still the better configuration for me at least. I use the gun as my "deep cover" gun, so that means that sometimes I am temporarily using an unconventional carry method,, like a pocket, or "Mexican" carry under a button up shirt, etc. While not ideal, this is usually only temporary and better than carrying no gun. The 13 offers three advantages for me.....first, I can set the safety on while I position the gun, then flick it off once it is in position. (3rd gens have what I call an "administrative safety" for safer handling, and should not be used liked a 1911's safety). The long DA first pull also is safer for unconventional carry. The third benefit is the short reset that the 3rd gen is famous for. If I have to pull my gun and shoot, the body on the receiving end is probably goin to be receiving at least half of the rounds in the magazine, if not all of them. The 13 is a real speed demon at emptying all 9 rounds in a short amount of time with a good degree of controllability. The 53 with it's longer reset is not as "fast" as a 13 or other TDA 3rd gen, at least in my hands.
This at least reflects my needs. The 53's and similar DA third gems are excellent. I'm not a huge TDA fan either, as my everyday primary carry guns are glocks with a very consistent trigger. But given the carry circumstances and my practice routine, my muscle memory seems to adapt to the 13's TDA as needed without issue. As I get more experience with the third gens, I'm feelin that the DAO's are best in the full size grip guns where you can get a better grip on them, like the full size 40's. YMMV, so pick the gun that is right for you. The nice thing about third gens is that there is a configuration for everybody, and they are all top notch excellent and high quality from the performance center guns, down to the homely 910