Being an opportunist during play I would suggest some things before going all "fire everything" on a player.
First it's a player, so mostly likely if not better, surely more unpredictable than any npc you've fought till now.
Second, check out his ship and armaments (UI button 1). If the target player has a better ship and weapons and armour than you, that is going to make it much harder to defeat.
Third if you have the equipment (kill scanner) and you see a small bounty, then it might not be a good idea to attack, since engagement between players usualy results in alot of damage, which costs alot to repair.
Unless you got the credits and are flying in a Sidewider then by all means go right ahead, but if in another ship the costs of loosing are higher.
Good luck.