Happy you had a good time at AD in Alor, Christian.
My prefered time for Raja Ampat is March to end of April. June-September is supposed to be more rainy (been in August, I can testify it is) but with better visibility (I didn't find though, or marginally), Dec-March is high season/high prices, people often say green waters as well. I can't say for october-november.
Re- Agusta vs. Cove :
Yes, I thinkAgusta is a little more expensive than Cove, however watch for promotions for Agusta, during the european diveshows they often have 10/20% discounts on periods outside summertime. I believe their peak season is aligned with usual school holidays in Europe ie. December-March + July-August.
Cove may bring you to the central parts like Kri etc. However it will be with a supplement also providing they find a minimum of divers to join in (I think min 6 divers).
Personally I 'm happy with both, photowise perhaps Agusta is on a better location and since Marco the owner is also a photographer, he can understand better needs, on the other hand Cove Eco have their own manta place for snorkelers, which is great and can arrange with private guide and own boat for a small family party.