Also, what's the plus and minus of tree vs herb? It seems like the tree is more expensive, and has larger flowers. Any other distinctions between them? Does one handle shade better than another?

As said, I have a few sunny locations, but I'd rather put these as close to partial shade as possible, as they will be competing with my lilacs which I also plan to plant in the fall.

I like the TP for the different colors it comes in, that herbacous Peonies do not. Yellow, lavendar, splashed red and white, both double and single flowers. Flowers are usually larger on the TP than the Herbacous. Mine get to salad plate size and larger! Leaves on the TP can vary in shape and lacy appearances. Herbacous are more alike in leaf shapes.

Herbacous do like the sunshine a lot, bloom better in sun. They can fill an area with foliage, make a boarder for you from naked ground, then be totally gone again in winter, with leaves removed in fall. Nothing is much prettier than a peony boarder just covered on flowers!! They take being ignored pretty well, make enough shade to keep most weeds and grass from choking them off, without a lot of need for constant weeding. Herbacous continue on blooming after the TPs are done. Using both give a nice long bloom time.

Both are fun to give away! They each last for many years of rewarding flowers. Cold doesn't bother them, not many problems to deal with so they look nice each year.

I would sure plant both types if I could!!