What a band does that a DJ can't
Spectacle. A great live band is an event in itself — people watch a band in a way they never watch a DJ, and a horn section hitting together is a physical experience no rig reproduces. If your picture of the night is people facing a stage, singing along to musicians they can see sweating, book the band. That instinct is correct and no DJ argument should talk you out of it.
What a DJ does that a band can't
Range and reaction. A band knows the songs it rehearsed; a DJ carries every era and lane your guest list spans and can turn the whole room in eight bars when the floor asks for it. A wedding floor that runs from grandparents to teenagers, across cultures, is exactly the room open format was built for — soul into afrobeats into 90s R&B into house, as one arc, in the original versions people actually know.
There is also the practical maths: a DJ plays for the whole night without breaks, needs a corner rather than a stage, and one professional costs less to put in the room than five. Bands break between sets — and whatever plays in those breaks is a DJ set anyway, just usually an unmanned one.
The hybrid, and how to choose
The strongest big-budget answer is both: band for the early spectacle, DJ to read the floor until close. If it is one or the other, choose on the guest list, not the couple — a crowd with one shared songbook rewards a band; a crowd whose taste spans decades and continents rewards a selector. And whichever you pick, audition the actual thing: full live footage from the band, a full recorded set from the DJ.