How long to wait between submitting books in different genres?

Submit the one you feel most strongly about. YA is a very popular genre right now. I can't speak for picture books, other than to say I've heard it's much harder to crack into.

Agents typically sign authors to represent their careers, not a single book. If decide to wait and submit the YA first and you get interest from an agent (ie, they ask what else you've written, what your career plans are), then you can mention the picture book. Of course, not all YA agents rep picture books, and vice versa. You've got some research ahead of you.

If you'd prefer waiting on the YA and trying to hand-sell the picture book w/o an agent, I'd wait several months before starting the YA agent hunt. See how the picture book sale goes first.

Since you don't need an agent for a PB, (and few rep them if I remember right), you might as well do both at the same time if you'd like. Query your YA to agents you like, query the PB to publishers you like. If you happen to find an agent who does both, you can always ask them about the PB after you've signed with the YA.

I just said this in another thread, but I queried 3 projects (2 different genres) at once. The project I would have put at the back of the line if I had to query one at a time was the one that got me an agent.

Query both. Write another one. Query it, too. Repeat until somebody gives you a break.