So I have some el cheapo Shimano brand new shimano BB's I have been using on my bikes (square taper UN26). Recently I bought a used frameset that already has a square taper BB. Being the conservative sort, I figure there is no reason to replace it if it still has life.
I was feeling for play and the spindle feels nice, no problems so no reason to remove it.

However when i took the cranks off my other bike to install on the new frame, I noticed the newer el cheapo UN26 BB on my other bike is a lot "stiffer" like slower to turn and more like molasses then the used BB. The used BB turns much more easily but there is no noticeable play or anything... which is the correct feel? I am just wondering if I should replace the el cheapo BB's on my old bike to something better or if that's just the way they should feel when new. For $11/BB I am not too concerned about how long it will last, but I don't want it to be sapping my precious power.

Bearings do tend to break in when new. Friction should reduce for a while. Hard to tell whether the new one will ever reach a point where it spins as smoothly as the old one, but not a huge worry.

For the frequency of BB replacement I experience, I typically spring for the un54 for bikes I'm going to keep.

Often on new bottom brackets, the drag is caused by tight seals which will wear in and smooth out after some use.

That's been my experience even with the higher end BB's. Between the seals, bearing preload and perhaps the excess grease in the bearings that gets pushed to the sides to let the balls run more freely new BB's can feel pretty draggy. Your UN26's will soon spin more freely. They may or may not eventually spin as nicely as the one in your newer frame and they may or may not last as long in poor conditions as the better UN54's.