Batman would probably win... mainly because the T-800 does not really have speed or agility to test Bruce's fighting prowess... now if a T-800 could connect on Bats it would easily affect him... but I don't see it happening... I see Bruce using his surroundings to eventually take out the Terminator.
The OP didn't even give Batman prep or weapons. They said H2H and Batman is faster? So you're saying a human Is gonna be faster than a machine? LOL....... Whatever dude. I see Batman thinking to himself " Ah I can take this guy down " and come to find out, Batman either gets thrown over a building or TERMINATOR just tears his entire body apart and Bruce is finished!
If Bane can paralyze Batman, then TERMINATOR can do the same and worse.....
Those T-800's are Gods.