Yeah, I'm sure I'll welcome that extra bit of reach on the "walk around" lens. I'm more concerned with whether I'll be happy enough with the 200 end of the zoom once I get it. I've been using a 50-150 on a crop sensor and been ok with that. But I'll be losing a little bit of that length at 200 now. And I always kept an all in one lens around for times I really wanted to stretch that length out more.
I won't lie... You might miss it a bit. But, the extra IQ on the 6D will give you more cropping room. So in the end, after some cropping, you might find you aren't missing it much at all.
In fact, on my camera, I have a 200/2.8 prime, and I also have the Tamron 70-300 usd, which is full frame. The IQ of the 200 is just so amazing, that I prefer using it over the Tamron, even when reach is an issue. (I did get a 2x teleconverter which I use sparingly as well).