I don't really see how it's a conflict of interest. The Realtor is interested in selling both homes at the highest price, in the shortest time. He's going to market both homes, and buyer's agents will make appointments to see both.
If his home shows better than yours... or is priced lower than yours... well, that's not really a conflict of interest, is it? If we're talking about your home... tell your Realtor that you'd like to "view" his home, since it's going to be competition with yours, and if you find it more appealing, you may want to consider if you should reduce your price accordingly.