I'm a little late to the party on these expansions, but it is only giving me the option to play with one or the other, or a standard game. I also have the game on PS4, and it allows you to use both expansions at the same time. What am I missing?

I'm assuming you mean the rulesets that you can choose when creating a new game.
the ruleset Gathering Storm includes all mechanics from Rise&Fall. So to use all mechanics available, select the ruleset Gathering Storm.

Thanks!

Btw, if you straight up disable** the R&F expansion, you will not lose the mechanics of R&F just as donald23 mentioned, you will however, lose all the civs, wonders, leaders, etc. that were part of the R&F expansion.

**By disable, I mean if you either turn it off in the mods menu, or turn off the DLC completely in Steam. If you do neither of those, and were ONLY asking about selecting rulesets, then never mind my post!