4 years ago my home passed electrical inspection with the range wired on a 10/3 wire in a 30 amp breaker. Today I am finishing out the basement and the inspector tells me I need a 40 amp breaker with a 6/3 wire. Has the NEC changed regarding this?

No, the code has not changed.
An inspector does not care what size range you put in. For all he knew you were going to use a dual-fuel range that would typically take a 30A circuit. It is NOT his responsibility to catch this type of violation. Whoever installed the range is at fault, NOT the inspector.

Is this a free standing all electric range?
If so then you do need either a 40 or 50 amp circuit. The size of the range does matter, but only if it is really big. By this I mean 12.5Kw or larger.

For a 40A circuit you can use 8/3NM, for a 50A or 60A circuit you can use 6/3NM.

It May be the Range, May even need 50 Amp breaker on #6. New Construction and remodel of Kitchen need 4 Wire Range receptacle and Cord. Existing can be 3 wire.
Need Specs on Range. Inspector may have noticed Range Name Plate.

I'm not sure if this is the information you are asking for but. Inputs @ 240V are 6,685 Watts

A circuit of 8/3NM and a two-pole 40A breaker are fine for this.