Most derailleurs don't care as the "brains" of the operation are at the shifter and a Deore LX will probably be a little crisper than an Alivio and both are index compatible if one goes that way.
Both will shift 8 speeds just fine and for the money the Alivio is a good deal as they seem to take a lickin' and keep on tickin'... I got tired of waiting for an Alivio to die so I could "upgrade" it although the upgrade to the XT did improve the shifting somewhat.
Front derailleurs are much simpler and even the cheapest front d will usually do a good job and better usually just means lighter.