The EB certainly has its problems, but it's a beautiful route. It depends on how flexible you are with your schedule. It sounds like you have time (and funds) to devote to a long trip - if so, I'd definitely consider the EB.
I've not ridden the CZ, but I'd love to. Having said that, my preference would be:
1) Coast Starlight
2) Empire Builder
3) Southwest Chief
However, if you haven't seen the Southwest and you'd really like to, taking the CZ west to San Francisco, then the CS south to LA, and the SWC back to Chicago would be a pretty good plan.
Then, if you really enjoy the trip, next time you could do EB to Seattle, the CS south to San Francisco, and the CZ east to Chicago. That way, you'll have seen 100% of the good scenery, and the best part (the CZ) twice - once in each direction.