Don't focus on UA vs. UAX (or any particular express contractor). Focus on the aircraft. The newer & larger versions of the '175, by way of example, have full-size OH, and it will be very rare to see "valet"-checking.

Bags which fit the sizer will fit the OH and depending on your BG, there may or may not be space. These aircraft have the advantage of 2-2 in Y, seating which ultimately works out to more space in the OH per passenger.

If there is other luggage which must be returned at the gate, e.g. wheelchairs & strollers, a good GA will, on request, slip you a green tag if you ask. But, don't count on it.