I am diggin the ATDI support here. I figured Jane's Addiction would already be running away with this.
In this situation, we finally have two bands I love. Jane's Addiction were an amazing band that none of it's members have been able to live up to in any way shape or form. They were another one of those bands that truly cemented the sound of the alternative rock to come before many others had. Legendary band that deserves the acclaim it gets for it's short lived span.
But I voted for At the Drive-In. For two reasons. 1) I figure Jane's Addiction is going to get way more support 2) I prefer At the Drive In.
At the Drive In are fucking amazing. Every one of their albums and EPs are chock full of amazing songs, and these guys clearly wanted to take punk into a new direction in the 90s. And they did that, paving the way along with bands like Fugazi for the entire direction that the post-hardcore movement has taken in music. They embodied what every fan of hardcore punk in the 90s wanted to create; music that had the ferocity of the hardcore they loved (but which was utterly dead by the 90s) as well as being unafraid to dabble in melody, progressive rock, and lo-fi ethics.
There will be people who will vote against them simply because of the Mars Volta. But the Volta is a completely different band from ATDI. Be warned, if you don't like punk or guitar-heavy fast music accompanied by melodic indie ballads, then don't even bother.
ATDI takes this for me, though I wouldn't blame anyone if they voted for Jane's Addiction here.