Alas, P. obovata and P japonica have are now considered as P. obovata. Both are woodland plants and do best in light shade and leaf duff/old compost.
To me what was sold as P japonica for years looks like a small tree where P obovata emerges as a clump of stems rather than a single stem. The japonica of old will generally send out a stem that will have a cluster of leaves at the top. The flower emerges from the center of this cluster. Obovata's flowers emerge as any other soft stemmed peony.
For me P. japonica has always been a late bloomer. Even appearing as late as July where P obovata is an early bloomer.
Either one is a good addition to your garden. You do need to not remove the spent blooms as part of the loveliness of both is the inside coloration of the seed pods when ripe and split open.