Using 1080i on a 720P monitor will produce better image/video quality?
Native resolution is always better than non-native.  If it only has a resolution of 720p, then it would have to be down-converting to that resolution which means it has to blend pixels which can produce artifacts from the pixel blending.  (Notably, softer edges is the most likely.)

Update: I'm sorry, re-reading, I noticed that it isn't native for either resolution.  I didn't read closely enough as I was a bit tired when responding just before bed.  Given that the resolution exceeds 720p, it would probably be better to use the higher resolution, though the interlacing would be the bigger problem.  I'd suggest trying both and picking whichever looks better to you.