You could have it all ! [Well most of it]
For me the west is far more interesting with it's abundance of National parks, including the Grand canyon and Yosemite, diverse scenery and open spaces. Plenty of 'Wild west'/desert scenery that's so different to what I am used to seeing in England and the likes of Las Vegas, LA and San Fran to keep you entertained.
Having said that you need to get a good size paper map of the USA and look to see what appeals to your party the most, as that's what is best and then follow it up with research here at RTA while asking questions as you go.
You could stil have your cake and eat it and drive across the country quite comfortably with a month, in fact if you want to keep on the move you could do a loop around the country and not have to face one way drop off fee's, by taking one route out and a different one back. That would split your day times by about 50/50 between driving and sight seeing.