Independant suspension is infinitely better offroad, in my opinion. It allows each corner to flex or compress independantly (Doh!!). Live axles mean that when one side lifts, it usually forces the other side down slightly due to the pivot point (A-frame) thus limiting movement overall and affecting speed of movement. Independant sus should be lighter, probably stiffer and always more adjustable than Live. Look at Ultra4 for instance, yes 'everyone' still uses a live rear axle, but there are so many IFS vehicles they'll soon outnumber the live all round.
However .. for production vehicles the independant suspensions are built to a price and are probably just cheaper overall than a live axle and a great marketing ploy!
In a racing situation I'd always (funds permitting) go for independant. In truth I doubt I'd ever be able to ...
When I raced model cars (don't laugh, they have more relative suspension movement and adjustment than most real cars) we often scratch built different suspension packages to suit different tracks or conditions .. Full 'proper' wishbone suspension almost always won the day offroad.
I don't know about on-road, not my thing really ..
