I don't think the frequency changes but since the parallel network has lower impedance than the series network, the gain has been changed and it may not oscillate or may not be sineusoidal.
If you're talking about the gain required for oscillation...
The standard Wien bridge (R1=R2, C1=C2) requires a gain of 3 to sustain oscillation.
With the network swapped around, I get a required gain of 1.5.
The problem with putting the series network to GND is twofold:
1. Positive DC feedback through the parallel RC network will cause the circuit to lock up. If you add a series cap,
2. you still have no DC bias to GND on the noninverting input.