Two great receivers. I have the Denon 3805 so you know what I like. That's quite a disparity from the the two quality bookshelfs to the RM6900. I think that you- and most other people would certainly be able to hear the difference. The LSi7's are wonderful sounding speakers. They will take you to places that the RM's never could.
One thing to remember about the Polk LSi line is that they are 4 ohm speakers - and are power hogs! They really need at least 100 watts/channel to bring them to life. The B&Ws will give you a lot more for the money, especially if you listen to classical music, with its complex sound makeup. As to receivers - I'd have to side with Riches1 and go with the Denon. The other suggestion I have is to check out PSB speakers - out of Canada. Great sound for truly modest prices. Look up the "Image" line - you can get speakers that have marvelous sound for much less than either B&W or Polk. PSB is part of the company that has the wonderful NAD receivers - one of which I just bought. And love!
I only have experience with the 6900. I'm just building my surround sound system. I purchased polk RM20's (same speakers as 6900 just different color) a week ago. After a few days I just wasn't happy with the sound and returned them. I got the polk RTi 6 for my front, CSi300 for the center and some RTi4 for the back. It cost a few hundred more but the sound was much, much better. The 6900 is adequate but certainly not very good. I think it's tough to buy quality speakers at that price point.