Honestly, since I'm playing in games that use both, I'm finding that I really don't like Group Initiative at all. I'm not really seeing it helping out all that much with posting rate and flow and it seems there are plenty of times (usually at the top of the round) where multiple players are posting at once, resulting in them having to go back and edit their actions, assuming they even notice the posts going up before their posts. If they don't, it adds even more wait time to the process. Assuming folks can keep up with the once-a-day posting rate, I think it should move along adequately. I'm also instituting a 24-hour rule where if a player doesn't post within 24 hours of my last post, I'll be assigning actions to their character.
I'd almost favor the fixed initiative option from the DMG where it becomes a passive DEX check and no rolling is involved for initiative at all.