My buddy has the 143D and its very similar in size/volume to my 13.0 Trib. The 156D is closer in profile to a 14' boat, just more length.
If your primary use is Missouri trips, I could see how the 156R would feel sluggish in the wind. I sure like mine on the Lochsa in bigger water or big III's with my kids.
Problem is that 160DD's and 156D's aren't as cheap or easy to come by!!
Do you need the full capacity of a big 16' raft? After now 10 years of rafting, my desired raft size is getting smaller. People who used to ride with me and loved it got their own boats, freeloaders stopped getting invited, my kids are getting bigger and like a splashier ride, and when it's just my family, a smaller boat is easier to carry.
(I went down from a full 16'x8' Maravia with 24" tubes to the 156R.)
By the way, cats are fun, too. [/enabler]
I'd recommend the 156D; the 160DD is going to feel a lot like your 156R.