I want to create a Rigger, and spare on Agility.
RAW if I use Remote Control I can shoot with Gunnery + Logic (according to Gunnery, p183), but with Rigger Control I have to use Gunnery + Agility.
What do I lose if I stick to Remote Control?
First, whether you use Gunnery + Agility or Logic for remote control is contested, see this question. If the abilities used in RC and rig-in differ, that is one thing you lose or gain, depending on your perspective/character. What is sure is that:
When jumped into a drone and in hot-sim, you can apply the +1 bonus to matrix actions to vehicle actions too, including firing mounted weapons.
Also, while the test uses the lower of your Data Proc. or the usual limit for the test (Accuracy here), you can add your control rig rating to it when jumped in.
Both rules can be found on page 266 of the Core Rulebook.