Both with a day of prep.
This is a spite....
At least remove the prep for the doctor.
Then it would be a stomp in favor of Batman. Anyway, this thread shouldnt be here since there are no anime characters in this bout, but that aside, The Doctor would win. Not only should he be smarter, but making him bloodlusted has effectively made him the most dangerous man in the universe since he has no morals and thus nothing to hold him back from doing whatever it takes to win.
While the same could be said about bloodlusted Bats, the Doctors TARDIS gives him the edge as it allows him to time travel and do what @KingOfAsh suggested. Additionally, a bloodlusted doctor could simply absorb the heart of the TARDIS, become Bad Wolf, and erase batman from existance altogether . and thats only two of countless methods the Timelord could use to put his opponent down.
Bloodlusted Doctor 10/10
So, Doctor in a murderous rampage, vs batman in a murderous rampage? Planet gets soaked in blood, Doctor is there,standing atop the tardis, waving bruce waynes head and taunting superman to have a go. Nothing can stop the doctor when he's mad.
Sensible answer though. The Doctor can overthrow centuries of planning with something he came up with while running for his life. Giving him an hour to plan ahead results in him curb stomping armies. A full day to prepare and I don't want to know what he'd do.