Should I accept to review a re-submission to a different conference (My field is Computer Science, where conference publications are the norm.)

I reviewed a paper submitted to conference A six months ago. The paper was borderline, and was eventually rejected. I wrote a reasonably lengthy review.

I've now been asked to review a re-submission of the same paper from the same authors for conference B. At first glance, the differences between the versions A and B are quite minor.

While I would have no problem reviewing the re-submission, I am worried about any bias (real or potential) that could occur from having access to a previous version of the work. This may be seen as preventing version B from standing on its own merits and having a "fair" shot at this conference. 

It's possible that my review of paper B will have the same comments as paper A, or at the very least my review will be written in a similar style. As such, while the reviewers are anonymous, it's quite possible the authors will realize the same person reviewed the two versions of the paper.

Should I accept this review, or suggest an alternative referee?
Yes, accept. You can start your review by stating:


  I reviewed version A of this paper @ [previous conference]. The differences between versions A and B are quite minor. My review remains largely unchanged: 


You can then provide a revision of your previous review.