I've done a few SkyKick migrations from SBS to Office 365, all uneventful. It all just worked.
None of my earlier clients cared about public folders. Now I have one, with 180+ GB in 14,000+ public folders. I split them up into top-level public folders all well under Office 365's 50 GB limit and started the migration. It all transferred in an expected amount of time, and Outlook sees everything.
OWA not so much. It sees all 50 user mailboxes just fine, but it only sees the top-level public folder names. No sub-folders, no contents. Microsoft Partner support has failed to get anywhere.
Public folders work on OWA on their old SBS 2008/Exchange 2007 system. In future they'll be using Dynamics CRM and SharePoint for what's now in public folders, but meanwhile they need their current public folders. Does OWA work for public folders on Office...