If you're purely looking at performance there should be no real difference between the two depending which model of MS390 you take.
The main driver that would steer you towards MS390 instead of the MS350 at this time is if your design includes L3 switching and Cisco Trustsec/Adaptive Policy. If these features are not in your design you could have a bigger case for the MS350's.
The issue with the MS390 is that it in fact is a Cisco Catalyst switch running Meraki software and the integration is not 100% smooth at this time.
Having said that, at some point all Meraki future switches will move to the Catalyst hardware model since the UADP chip offers more future proof features.
So your choice is between a mature and stable platform vs a young, promising but beta platform.