The difference is, AC switches are powered by AC and DC switches powered by DC - duh. Only kidding!
Joking aside, often that's actually the only real major difference. Some switches have the option of using AC or DC power modules, some even (I recall?) even allowed redundancy using AC and DC power modules.
I believe, generally, AC power can provide more wattage. I.e. you may find you can support PoE ports using AC but not DC.
Also, generally, your switch options using DC tend to be much more limited.
Again, otherwise, no real difference in switch capabilities. (Remember, internally, the switch generally uses DC.)
A situation to use DC? If the location already uses it. Not as common now a days, but (again, I recall?) "older" TelCo equipment often ran using DC, i.e. locations where you'll find NEBS certified equipment. So, if you wanted to place a data switch in one of those racks, it made life easier if it too could be powered by the DC already provided to the rack.
A interesting problem presented to me, several years ago, was a location using mostly DC. They had extra DC capacity, but not any additional AC capacity. We couldn't find a suitable small switch that used DC. I suggested using an AC switch with a power inverter (changes DC to AC). Don't recall what they finally decided to do. The other alternative was to electrically upgrade the site's AC capacity (which required much more time and much more costly).
