We looked at both. If we had ended up getting married in Vegas, I think we would have gone with the Flamingo. They have some gorgeous areas set amongst lush gardens, which makes it pretty private. It also worked with our budget. Caesars was really nice as well, but the area that we were looking at (Venus garden I think?), my FI was not comfortable with, as you could view it from the bar/restaurant next to it. Go figure we are now getting married on the beach, in plain view of anyone who wants to watch!!
Another place we were considering was at the Bellagio. You can get married on the terrace, and they play the fountains for your first kiss.