Depends on what pistol you're talking about. A V1 USP is totally different than a V1 P30 or P2000, etc.
V1 on a USP is a DA/SA trigger with a safety/decocker on the left side of the frame. This is one of (if not the) most popular variants for the USP for right handed shooters. It allows cocked and locked carry, or DA/SA carry. Some do not like having a decocker as they prefer to ride the safety when shooting or just fear accidental decocking and go with a V9, which is safety, no decocker.
V1 on a P30 would be the light LEM trigger.
The LEM trigger is a pre-cocked DAO trigger. Each pull is the same and can be had in various weights from 4.5 to about 7.5lbs. The pre-cocked aspect makes it a light pull with some stacking at the end before it breaks releasing the hammer. The slide cycles and once again it's pre-cocked. However, it is not pre-cocked in hammer as the hammer is down and only when you pull the trigger will the hammer begin to lift. I believe it is a spring that gets pre-cocked allowing for the light pull making the lifting of the hammer easy and light. If the slide is not cycled (such as when dry firing without racking the slide, or failure to recoil fully when firing) the trigger will operate as a full weight DAO pull since there is no pre-cock to lighten the pull.
And yes, the variant is really a matter of preference.