Advantages the mini has over the Chromebox: memory upgradable to 16 gigs (Apple says 8 gigs, but others report that 16 gigs works) whereas the Chromebox's memory does not seem upgradable at all; Firewire and Thunderbolt ports whereas to attach an external drive to the Chromebox your only choice seems to be slow USB 2; storage upgradeable (specifically, you can add an SDD or a second hard drive to the mini).
How repairable and upgradable the Chromebox is I do not know -- googling for "chromebox teardown" finds nothing interesting. iFixit gives the mini a relatively-high repairability rating of 8.5 (but adding a second drive to the mini requires an expensive custom cable).
Size and weight are very close. Both have the power supply inside the device.