Both of them would provide good results as they are both compound lifts that not only load the upper body musclature,but the abs and lower back because they help stabilise the body.It would probably be better for a newer lifter to become proficient at the overhead press first then switch to push press if you needed it.
my personal preference is the push press. its more explosive, allows more load and involves more muscle groups. also for me it seems less stressful on the shoulder and rotaters.
It seems to me that one would almost always chose push presse since the same work would be performed to lift the bar and more load will be available for the static hold and negative.
yes. by chance are you running a 5x5 program or something similar? imo the push press seems to be more synergistic with that type of training, for the reasons i mentioned in my previous post