Look at the datasheets!

The [LMC6062 datasheet][1] 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][2] 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. 


  [1]: http://www.ti.com/lit/ds/symlink/lmc6062.pdf
  [2]: http://www.ti.com/lit/ds/symlink/lmc6482.pdf