Few things to ask:
- How actively does the VC (and the partner who is joining the board specifically) like to get involved and what sort of topics do they care about the most? 
- What happened when there was a disagreement between VC and founders? How was it resolved? (a wedge issue) 
- What areas has the VC helped the most? What areas do you feel like they could have helped more? 
In general, if you're giving up a board seat you really want to make sure you're bringing on someone who is completely in line with your vision of the company for the next 5+ years and can help you get there, especially if there are gaps in founder's backgrounds.

