Well, electric batarangs are at least an improvement and might actually damage Vader. Would an electric current travel down a lightsaber blade?
Technologically, even if Batman had enough time to prepare and had access to the Star Wars galaxy, I'm not certain he would have a technological edge. Batman is rich, sure, but Vader has the full force of the Galactic Empire. Batman isn't going to his hands on a Death Star. Pure technological edge would have to go to Vader (ingenuity to use them is another story).
Swordsmanship - Vader wins by virtue of lightsaber. Of course, if Batman has a lightsaber this is a much bigger threat. But still, lightsaber fighting is different from typical swordsplay, and Vader would still have a lifetime of experience at his head. Batman has a very uphill battle here. In the end, I believe Vader's Force-adeptness will save the day. It's not the same as precognition, as Eerongal pointed out, but trusting the Force does allow much greater lightsaber power. As in, they deflect more blaster bolts than you can shake a fist at.
Physicality - Batman wins. He has trained much harder than Anakin ever did. Even if Vader has cybernetic enhancement above the normal man (which is disputable at best), Batman has the upper hand. However, I'm not sure it matters.
Stormtroopers - Yes, Batman can defeat regular guards without much effort. Still, blasters give Stormtroopers the possibility of at least some life. Given a proper troop of Stormtroopers in formation around Vader, hopefully in some place which isn't too enclosed, there's no way Batman would dodge all of them. Furthermore, Batman doesn't use guns, so it is unlikely he would use blasters. He could have a lightsaber, but I doubt his adeptness with it.
Stealth - Batman's greatest strength, besides his own ingenuity, lies in his power of stealth. In any remotely neutral ground, Batman will be able to get the building's floor plan, which is definitely a big boost to Team Batman--note this advantage would obviously be moot in any Empire structure which also carries Vader. Still, Batman has an uphill battle. Vader would mostly feel a Force disturbance with Batman's presence, and thus increase his security. It would be unlikely Batman could get an easy hit on Vader. He could, however, dispatch Vader's Stormtroopers easily. The disadvantage is that he would reveal himself to Imperial troops. Also, the second Batman reveals himself he would need to get out his presumed lightsaber to defend himself. Lightsabers are not immensely stealthy objects.
First Strike - Batman will strike first. As already stated, Vader would already be on Batman's hit list, so Batman would be working out his plans to strike. But Vader has no need to personally hunt Batman down, ever. Vader will wait for a new Death Star and just annihilate any planet Batman was presumed to be on. Destroying innocent planets? Doesn't matter. It will only make Batman want to destroy Vader that much more. And if Batman strikes first, which he undoubtedly will, Vader has home turf advantage.
I suppose that depends on whether Vader knows Batman is in their galaxy, but this isn't an issue. I mean, come on, in Soul Calibur 4, Soul Edge caused a big enough Force disturbance that both Vader and Yoda decided to go to 16th Century Earth. Batman, with his extreme obsession, entering the Star Wars galaxy would create a sufficient disturbance for Force users to feel, especially Dark Side users.
Turf - If Batman escapes Imperial assaults long enough, Vader will have empirical evidence of Batman's skill. There's no point for Vader to take on Batman alone. Vader may as well just wait with the Emperor.
Stormtroopers + Vader + Palpatine will always defeat Batman + lightsaber, no question.
