Are you talking an off the shelf AIO, or custom loop?
Generally speaking, an AIO should outperform an aircooler at a similar pricepoint, usually not by much though.
AIO's look a bit cleaner vs bulky air coolers, and are a better idea for any system that'll be shipped, or moved often (vs a large air cooler hanging off the motherboard).
On the flip side, they add additional points of failure in the pump, and potential for leakage. If something 'fails' in an air cooler, it'll be a fan - and an easy replacement. If something fails in an AIO (other than a fan), that necessitates a full replacement of the AIO.
Custom loops are a labour of love. They should be the top performing option, but they're expensive, require regular maintenance, and are not particularly 'easy' to get into.
For someone just starting out, a quality air cooler would be the route I'd suggest going.