Migration Assistant won't transfer files from 10.8 to 10.9
You shouldn't have any problems if you use Firewire/Thunderbolt Target mode (hold T at startup). Depending on what ports you have you will need a Firewire 800 cable or a Thunderbolt cable, or Thunderbolt to Firewire adapter if you're transferring to a newer Mac without a Firewire port from a model with a Firewire port.

I've just tested this with a dummy account on a 2011 MacBook Pro running 10.6.8 transferring to a 2012 MacBook Pro running 10.9.5 - via Firewire - and it transferred fine with no errors.