Both fill a room with fragrance. They do it differently enough that most homes end up using both, for different rooms and different moments.
Scent throw: melts win
A candle burns its fragrance oil along with the wax at the wick. A melt has no wick — the wax is warmed gently from below and the fragrance evaporates rather than combusts. That means more of what you paid for reaches the air. In practice a melt of the same fragrance load will noticeably out-throw a candle of similar size.
Cost per hour: melts win, clearly
A standard melt gives roughly 8 to 12 hours of usable fragrance. Six of them cost about what a mid-range jar candle does, and give several times the fragrance hours. Melts are also reusable until the scent is spent, and you can burn half a melt in a small room rather than committing the lot.
Soot and residue: melts win
Nothing combusts in a burner — the wax is warmed, not burned — so there is no wick, no smoke and no soot mark on the wall above it. Candles, especially in tall jars, can tunnel, mushroom the wick and leave a dark ring. Melts sidestep all of that.
Ambience: candles win
Nothing about a melt replicates a flame. If the point of the evening is the light rather than the smell, a candle is the right object. Cut-out decorative burners close some of the gap by casting patterns on the wall, but they are not the same thing.
Control: melts win
You can change scent daily with melts. A candle commits you to one fragrance for forty hours. You can also blend two melts in a single well, which is not possible with candles — see how to layer wax melt scents.
Safety: a draw
Both involve a naked flame — a wick in one, a tealight in the other — so both need the same care: a heat-resistant surface, clear space, and never left unattended or burning overnight. See burner safety.
Mess and upkeep: draw
Candles need wick trimming and can tunnel if you burn them too briefly. Melts need the spent disc lifting out of the well. Neither is arduous. Soy melts are the easiest of all to clean up — see how to clean a wax melt burner.
The short answer
Use melts for everyday fragrance, for large rooms, and anywhere you want to change scent often or avoid soot marks. Use candles when you want the light. Most people who try melts properly end up buying fewer candles, but not none.