Vicky29
The main advantage to the non-inverting configuration, as shown in your first crcuit, is high input impedance. The input imedance is equal to the open loop input impedance of the op-amp times the loop gain. One disadvantage is that the common mode rejection ratio must be taken into consideration, since the op-amp input does not stay at virtual ground. I see no advantage to your 2nd circuit. You are going to amplify any errors incurred in the first stage by the gain of the 2nd stage. Also the input impedance of the 2nd circuit is 10K, vs darn near infinity for the 1st circuit.
Regards,
Kral