If you don't want to stream both simultaneously but switch from one the other, you don't need 2 installations. That's what profiles and scene collections are for (Menus Profile and Scene Collection).
You create one profile for Twitch and one profile for Picarto. In the Twitch profile you connect your Twitch account, and in the Picarto profile you enter the Picarto streaming settings. If you switch profiles, you switch the streaming settings as well.
If you also need different scenes between the two, create one Scene collection for your Twitch sessions, and one scene collection for your Picarto sessions.
You can either switch manually with the menus, or you can also create desktop shortcuts that directly load a given profile and/or scene collection. I assume you called your twitch profile "Twitch profile" and your Twitch scene collection "Twitch collection". Create 2 copies of the existing OBS shortcut on your desktop and name one copy Twitch and the other Picarto. Open the properties of the Twitch shortcut, and in the link properties locate the Target entry. Append one space, then
--profile "Twitch profile" --collection "Twitch collection"
The complete target line should look like this:
"C:\Program Files\obs-studio\bin\64bit\obs64.exe" --profile "Twitch profile" --collection "Twitch collection"
Do the same with the Picarto profile, collection and shortcut, accordingly.
Now, if you double-click one of the new shortcuts, OBS will start with the corresponding profile/collection already loaded.
Reference: all launch parameters
https://github.com/obsproject/obs-studio/wiki/Launch-Parameters