Which auction do you think you would be more likely to get a better price on something? Same item in both auctions, lets say a 1921 Morgan Dollar graded MS63 by PCGS, same auction terms, bp, shipping...... 1. An auction that has a lot of items and a lot of bidders (over 100k items and over 100k bidders) or 2. An auction that has fewer items and fewer bidders (less than 1k items and less than 1k bidders)
Poll options do not include 'no difference' so your results will be skewed by the omission of all the people who don't think it makes much difference either way. The inclusion of the neutral option might show that those expressing an opinion for one or other option you specify represent only a tiny fraction of those with an opinion.
If people are looking for something specific, larger auction attracts more attention. But for people just browsing for something they may want only when they see it, a lot of it can get lost amongst the masses of items.
If the ratio of buyers to lots is a constant the average prices should also be constant assuming that there are no other factors operating.
Are you asking from the perspective of a buyer or a seller? I think a seller would want the broadest possible audience (with more potential bidders) while a buyer would want a smaller auction with less competition.
I agree with more choices. A lot of it will have to do with how good the rest of the coins are. I have made some great purchases at large auctions that were mainly junk. No one wanted to sit through all the dreck so I was able to make some good buys. I have seen some small auctions be filled with tremendous quality, so every single coin got lots of attention and bids. In a perfect world, I would say a large auction filled with high quality items. Such a sale would have the attention of every collector of that series, so my potential bidder pool would be the largest possible. That wasn't your question though.
I like buying at the auctions with 1K bidders on 100K items, and selling at auctions with 100K bidders and 1K items