I get the beats matched and lined up with both ears in the headphones, then as i bring the new tune in i slip one ear out of the headphone so I can hear the monitor. I find it really hard to beatmatch without using both ears in the headphones when playing out.
Cue 1 ear in 1 ear out when Its locked I totally take the headphones right off and listen to the monitors as thats what the crowd are hearing and you can hear the eqing better than havin something in your headphones
It doesn't just depend on the environment it depends on the style and quality of tunes your mixing as well.
When I'm playing my own tunes I generally have both tracks fully cued in the headphones and will sometimes do a little beat matching in the headphones before putting one ear on the monitor and brining in the track. Often I will do away with the headphones all together once I can hear the new track pushing through on the monitor.
When I'm playing B2B I'm more inclined to use the cue / master fader to help me check things are lined up and balanced.
If you really want to stay in touch with the crowd I think it's important to do away with the headphones as much as possible, I'll often put them aside while selecting tunes etc.