Broad&Deep is the ideal answer.
On amateur level both approaches should work, while it's increasingly rare to see titled players relying on only a limited repertoire that they know in depth.
I remember Malakhov once saying that his approach as Black was to stick to one defence at a time (against each first move, obviously) and just know it better than everyone, while as White it was more important to be flexible and unpredictable in order try to catch your opponents where you think they are weakest. Presumably the logic is that White doesn't get a meaningful advantage anyway, especially if Black gets a kind of position he wants and knows, so a psychological "play the man" approach is needed, while as Black it's more important to be theoretically OK and really familiar with the positions in order to reduce the risk of losing.
I do this to some extent in that I vary quite a bit with White (with 3-4 different first moves, though 1.d4 more often than the others), pretending that I actually know enough to pull that off without bluffing! Of course the point is the same as Malakhov's: To look at the database, find some weakness in my opponent's repertoire and/or style, and try to exploit that.
As Black I ideally want to have at least two defences against both 1.d4 and 1.e4, one sharper and one more solid (Malakhov's singular approach may work less well if your only defences are really sharp and unbalanced). But the reality is that my sharp defences have stayed with me over the years, while I keep cycling through more solid/mainstream defences without settling on any long-term. This lack of solid defences to fall back on, ones I really know and understand, hurts me against stronger players...
Apart from this talk of the ideal approach, in reality I find it hard to resist looking at whatever openings I find interesting at any given time. Recently I've had a French Defence binge despite officially having given it up (except in blitz) and having two other defences to 1.e4 I do well with. This forum also triggers my undisciplined opening studies. Well, sometimes I just have to follow my interest instead of fighting against it.