Look at the datasheets!
The datasheetLMC6062 datasheet says on page 3:
Input common mode voltage range: \$0..V^+\$ − 2.5V
i.e. at \$V^+ - 1V\$ you are already 1.5V above the range that is guaranteed to work.
The LMC6482 datasheet on the other hand says it is a rail-to-rail input and output OpAmp, i.e. it works with input voltages from GND rail (0V) to up to the \$V^+\$ rail.