Pros: Lots of output flow options (spraybars, adjustable angle nozzles), generally allows for more thorough filtration, imo. (more water-to-media contact/less bypass, it seems, though I could be wrong), potentially quieter, generally fewer technical issues from my experience (my HOB impellers get stuck from time to time, for no apparent reason, especially when starting them up after a water change). Depending on how you set it up, you can potentially do waterchanges using only the intake/output valve(s) rather than getting out a siphon (you just have to have both the intake and output set so that they're below the desired water level during a water change).
Cons: Maintenance generally requires numerous steps (shut off intake/output valves, drain canister, remove lid, rinse media, refill canister, reassemble, reopen valves, then, for non-self-priming models, you have to prime the filter (typically either by pouring water directly into the intake tube, or by pressing a button several times before plugging the filter back in). Granted, you get used to the process after a while and it's not a big deal, but it still takes longer than cleaning an HOB no matter how you do it.