Re: ST-10- 37 or 44mm objective?
37mm will mount lower of course, assuming the eye piece is not the limiting factor (interfere with bolt).
However, at 10x, the 37mm will have a 3.7mm exit pupil vs. 4.4 of the 44mm. 3.7 isn't bad, but it's nice to keep it at 4 or more in my opinion. Then again, with that quality of glass in the USO I wouldn't worry about it.
I'd probably go 37mm as I can't stand high mounted scopes. I like keeping them as low as possible.