Inverting summing amplifier vs Non-inverting summing amplfier
I'm only going to bother with the main con of the non-inverting summing amplifier because it renders it fairly useless in many applications. So....

The big disadvantage of the non-inverting summing amp is that if you disconnect one of the inputs, the gain of the circuit doubles for the remaining connected channel. This is not the case with the inverting summing amplifier because it generates a virtual earth summing point.

Implications that follow: -


Disconnect all the inputs and the non-inverting pin is floating (bad)
Add a third input and the gain of the original two channels drops (could be bad but in other applications could be good)
Any source connected that has a variable output impedance will vary the gain of the other two channels (probably bad)
There is cross talk from one input to all other inputs (may or may not be serious)


None of the above happens with the inverting summing amplifier.