Actually we don't use closed loop gain to determine bandwidth using GBW. What you should use is the Noise Gain.
Bandwidth = GBW/Noise Gain
Where Noise Gain is defined as 1/Beta Beta being the feedback fraction which is equal to R1/(R1 + R2) for both the inverting and non-inverting amplifier configurations. (R2 being the feedback resistor).
For a purely resistive feedback network, the Noise Gain plot is a horizontal line on a Open Loop Gain vs Frequency plot and where it crosses the Open Loop Gain plot the loop gain is equal to unity. At this point the closed loop gain is down 3dB.
Lets consider a non-inverting amplifier with equal resistance values for R1 & R2 and it having a GBW of 1MHz.
Its closed loop gain is equal to its Noise gain which is equal to 2 and therefore its bandwidth is 500kHz
Now lets consider an inverting amplifier also with equal resistance values for R1 & R2 it also having a GBW of 1MHz.
Its closed loop gain is equal to 1 but its noise gain is equal to 2 therefore it also has a bandwidth of 500kHz.
So it is apparent when comparing the inverting and non-inverting configurations of amplifier with equivalent closed loop gains that the non-inverting amplifier will have the higher bandwidth.
In fact if both configurations of amplifier are configured for a closed loop gain of 2 then the non-inverting amplifier has a bandwidth of 500kHz but the inverting amplifier, which now has a noise gain of 3, only has a bandwidth of 333kHz.