Ccleaner found and removed many elements staying after the KASPERSKY removing with Add/Remove. So I don't think there are interactions between the 2 antiviruses now.
I can prove it : after uninstalling KASPERSKY, I installed AVAST 5 (until the problem with WMP11 be resolved), and Youtube worked exactly like before installing KASPERSKY, so not very fast, but a little faster than now.
Since I installed the full AVAST 6 version the videos load slower.
edit : I just checked my connection speed, it is approximately 7.5 Mbps now. But Youtube videos still load slowly