Using LSII PJ during outdoor, you need to point the dome to the subject, so no different for which version you are using.
btw, at outdoor, if you subject is far away, you are better off with shooting direct flash.
Outdoor, don't really need to get the extra lightsphere as fill flash. The Diffusion Dome will be good enough. Adjust your flash EV output when necessary.
I got a cloudy one just in case I need to shoot indoor. I prefer to use f/1.4 lens so the cloudy one is ok. If you shoot indoor group photos, use a clear one. Use it as a bounce light. The colour is more neutral. The cloudy one absorbs more and causes a warmer effect. Bring your camera and try both at the shop. Ask someone to stand near the wall and shoot. See which one you like better. For general purpose I'll choose the neutral one. IMO, you should save the money.
either is fine. if its bright and sunny, suggest shoot without LS. if back face the source of light, say the sun, then the flash and LS will come into good usage. or u might jus like to use the flash with the LS in outdoor for that extra sparkle in the eyes(catchlights).