I have a choice between mid-July and the last week of August for a biking/hiking trip in these parks. Does anyone have an opinion regarding which is better?

Hard call. Crowds are fewer in late August, days are longer in July. We were there last year in mid Sept. It was perfect. We stayed at Signal Mountain Lodge and would go again in a heartbeat! Have fun.

I think my choice would be for the last week in August, although post Labor Day would be even better in terms of crowds. I have been there in early September and the crowds were thinner than in July, using last year as a basis for comparison.

I think that late August would be more similar crowd wise to early July, with the threat of really hot weather less in late August. (Last August was particularly brutal heat wise.)

Many public schools are back in session by late August and that exodus thins the crowd a little. On the other hand, as the summer crowd flows out, many late summer tour groups on big buses come in.

The tour bus brigade does not usually take to the trails more than 500 yards, nor do they linger in the geyser basins.
One look at Old Faithful then back on the bus for the next glimpse. (Editorial comment here. I don't call that visiting the park. I think viewing is a better term.)

You will find hikers there all season long.

That is my view at any rate. Now let us read what the others have to say.
I usually like to see if my views stand up to the consensus.

OOPS mis edited the line above.
I meant to say that I think late August would be more like early September than it would be like July. July normally is more crowded. Hopefully some diminishing of the crowd size is evident in late August.

I agree with Bob Brown. I would recommend late August, with crowds likely to be smaller. And yes, early September is even better! Besides the crowds being smaller, you have added pleasure of experiencing the fall foliage.

Thank you for the opinions. I was hoping that the schools might start early and the last week would be less crowded. I would prefer to go in Sept but the trip is not offered then.

We plan to visit Yellowstone and the Tetons in the fall. I was thinking late Sep/early Oct. This time of year has worked out great for hiking in Utah but for Yellowstone, what is the weather like? Would you recommend moving it up to early/mid Sep? We want to go after the kids are back in school but while it is still nice enough to day-hike for 7 days. Thanks!

Yellowstone is not a hikers park, at least not like others. October? Much of the park is closed by then.
The Old Faithful Snow Lodge is open until Oct 16.
The Lake Lodge closes 25 September;
Old Faithful Inn is open until the 14th of October.
Canyon closes 18 September.

Temperatures by mid October in Yellowstone can be nippy.
50 average high; 20 average low.
But if you get cold, there is always a hot spring around to stick your feet in.
(The rangers don't like it however.)

We were there last year the last two weeks of August and had good weather and few crowds.

Bob - Thanks so much for the great input. My reference point is hiking Utah, which we usually do in October after all the tomatoes are harvested in Minnesota. So I guess I will have to either consider early September or consider another park that's more like Zion or Bryce, which we loved.

Weatherwise, early September is great in the Teton and Yellowstone.
The Teton is one of the best national parks for hiking.