Overall, it's still Spidey in a state of the art bullet proof suit equipped with a highly versatile set of tools/gear designed to be used by a much weaker person. Should take Spidey less than an hour to fashion webshooters from Bruce's superior tech available in the batcave and make himself at home in the armor.
Batman will be equipped with a bullet proof armor designed for a MUCH stronger character and (to my memory) was heavy enough to slightly affect the mobility of this person as well as web shooters that take a person far stronger/agile in order to use effectively.
Batman gets the advantage of intel, investigative skills, superior strategy and tactics as well as familiarity of environment (vs Spidey but NOT Spidey's villains as he'll be taking them on in their turf). Spidey villains will use overkill attacks vs Bats as they will be expecting to face a superhuman opponent.
And Spidey obviously gets his super strength, super agility, spider sense and high durability, higher stamina and healing factor against villains who will NOT expect to be facing a much stronger/faster/durable opponent. Joker (the most dangerous opponent) will not be aiming to kill from the get-go as he'll still believe he's facing the bats (for the first 5-10 seconds anyway).
I still say Spidey ftw. 😛