How much time are you taking for this trip?
Having been to both national parks, I can tell you that I enjoy the parks much, much more when we finally figured out to SLOW down. We saw more in-depth and enjoyed it more and we did a ton of stuff that most people never do.
I talked to a ranger in YNP and she said that they estimate that 95% of the park visitors never get farther than 100 yards off of a paved road in YNP.
Once she found out we were actually interested in putting in a little work to see more, she tipped us off to some places like a valley where hundreds of bison had been gathering. It was quite a site, well worth the 30 minute hike to get in there, but nothing you’d ever see from the road.
If you REALLY want to see two NP in one trip, have you thought of YNP and Grand Teton?
The trout fishing in both YNP and GT is terrific, if you can put in the time to get away from the roads.
Grouse