I believe rapport has some anti keylogger and browser integrity check functions that avast free doesn't have.
As has been said, with the dedicated isolated safezone browser in AIS there is probably no need for these (and anyway rapport won't load into safezone, nor will any other browser security plug-in).
Safezone protects the browser it uses (Chromium) and prevents any keylogger access. Safezone costs, rapport is free. I couldn't tell you which is better.
Your bank may have views on what security they prefer you to have of course, which I would guess may in some cases influence their opinion on whether you had taken reasonable steps should the worst happen.