There is a world of difference between auto-resolve and normal tactical combat. Units don't appear to need to move, for one thing. This can cause a high combatspeed unit to attack and wipe out every enemy unit in one turn (or archers to become completely useless). Another big difference is units aren't limited with their counter-attacks, any attack against them will cause a counter-attack. This makes auto-resolve dangerous on high difficulties, where you can go up to a guy with 3x the force and still lose because of that (15 counter-attacks in one turn? NO PROBLEM!). A third glaring issue is that noone seems to use abilities or spells in auto-resolve, they just chop away (makes any special units useless, like dragons).
There are also major issues with how damage vs armor is calculated in autoresolve combat. For example, a 4man lord hammer unit can completely fail to damage a 12man leather-armor-wearing unit (all damage gets "absorbed", whatever that means).
I don't use it ever, except against monsters in late-game. It is practically cheating.