Given my druthers with all other constraints aside I'd go for 4-wheel, fully independent, continuous-turn swerve almost every time. a well-executed swerve beats most other pretty readily as far as widest applicability and best performance across the board. That said, there are other constraints, though they affect different teams and games in different ways.
Cost: A well-done pivot drive is almost always more expensive than mecanum or omni. In fact, if anyone's succeeded with a cheaper version, I'd love to talk. Pivot usually (though not always) requires milling, and of course more motors. After pivot, mecanum is usually more expensive than omnis, just by virtue of the wheels themselves.
Building/Wiring Difficulty: Everything's as difficult as you make it. That said, it's a lot "easier" to make a pivot drive complicated than an omni drive. That's not to say many teams don't make creative and effective omni, mecanum and other holonomic drives as well. However, from fabrication to wiring to programming, pivot drive is a tall order. I've never heard of a team with a successful pivot that didn't start examining the possibility in pre-season (then again, this is helpful for almost any type of success).
Programming: A pivot drive is certainly more complicated than a just simple tank, but how far you go with it is really up to you. We currently have crab, spin, x- and y-biased snake, x- and y-biased auto, and x- and y-biased tank (all with arbitrary fronts) at various levels of development. Depending on the game, a decent crab and/or snake can be more than enough to facilitate successful driving.
Traction: A good pivot works wonders here. Mecanum lacks in the area, as do omnis wherever they're used. (If you use omni front wheels and traction backs, you're pretty easy to push up front.) Perpendicular/angled wheels suffer here too, as you're effectively sliding the wheels' projection not along your movement vector.
Another novel idea: Last year, my team went with a 6wd wide configuration with a 7th deployable wheel in the back lowed to lift up the back 4 wheels. On the regolith, this allowed us to break more easily (transverse coefficient was greater than inline), spin quickly, and if we were lucky, move sideways. Of course, this all depends on the friction coefficients and their ratios, but suffice to say there are other options--notwithstanding
nthdrive.
But if we're talking truly versatile, I've got one word: walking!
We never play to lose, or even go easy. We play our best every match. - Paul H [more] 
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