It isn't really an either-or, and most couples work that out on their own. But there is one thing a live player does that a playlist cannot, and I discovered it on the evening everything went wrong.
A wedding where the rabbi simply didn't arrive on time. The reception stretched on and on, my repertoire had already come full circle, and — to be honest — I was starting to get bored. So I began to improvise. Whole passages, built on the harmonies of the backing track running underneath, with no actual song beneath them. I watched people listening carefully, trying to place where they knew it from. Nobody knew I was inventing it in real time and thoroughly enjoying myself. A playlist cannot do that, and events run late almost every single time.
Moments. The ceremony, the bride's entrance, the reception, the first dance. A live player stretches a passage when the bride walks slowly, drops the volume the second the rabbi starts speaking, and lifts precisely as the glass breaks. A playlist plays what was recorded, at the tempo it was recorded, even when the room has decided otherwise.
Dancing. When it is time to lift a hundred people for two solid hours, a DJ with a powerful system and seamless transitions is the right tool, and their range is limitless. I don't compete with that and I don't try to.
They combine. Live music for the reception and the ceremony — the part where guests arrive, mingle and feel something — and a DJ for the dancing. It is also the combination that makes the most budgetary sense, because you are paying for live playing exactly in the hours where it makes the difference.
I'll say this even though it doesn't work in my favour: "live musician" guarantees nothing. Some players simply don't sound good, and there is such a thing as technically flawless playing that does nothing for anybody. How do you check before you book? Ask for a live recording from a real event — not an edited video with studio sound. Hear what it sounds like in a real room, with background noise and people talking. That is what you are buying.
If you are combining, the musician and the DJ should speak before the event: who plays what, when exactly the handover happens, and who owns the sound system. Five minutes of conversation prevents the awkward moment where both sides wait for each other in front of a silent room. I always initiate that call myself.