Comparing the acidic strength, the nitro-substituted group is definitely more acidic. This can be reasoned by fact that a higher delta positive charge which develops on the H due to the strong -M nature of the nitro group. Another way to check the acidity is to check the stability of the conjugate base.
The conjugate base would be the carboxylate ion which being a -M group creates a lesser electron density at the ortho and para positions. This positive charge is however stabilised by the methoxy group, which is a +M group, and destabilised by the nitro group. So from this viewpoint, the methoxy derivative should have been more acidic.
Why is this not so? What is the fault in my reasoning?