Batman is the world's greatest logical thinker and detective. Deadpool is a mutation whose constant state of being both the sickest and healthiest person at the same time has scrambled his mind so as to be totally devoid of common sense and sanity.

Batman has a strong moral code and martial arts training from the world's masters as well as an arsenal of million dollar gadgets. He, however, does not have any enemies totally devoid of an orderly mind. Even the Joker has some semblance of order in his mind.

Deadpool is a skilled killer with no moral or honor code whatsoever who does things how he pleases and has a totally random thought process, if you could call it a process since it's totally random.

Who would win? Even without the immortality taken into account I bet on Deadpool. Mainly because unlike the Joker... Deadpool is a skilled killer who also doesn't even have a tiny bit of predictability or sense.