I personally would recommend straddling the season.
Several years ago, I spent about a week at Yellowstone National Park and Grand Teton National Park over Memorial Day weekend. Before that weekend, the parks were not crowded — but then, certain venues were closed. After the weekend, it was noticeably more crowded — but then, everything was open.
If you plan your trip right, you will get to enjoy the best of both season and off-season.