None of the comparison operators are case sensitive by default. Each of the comparison operators has two additional variants, one which explicitly states it is case-sensitive, and another which explicitly states it is case-insensitive.
For example, the following statement returns true:
'Trees' -eq 'trees'
Adding a c modifier in front of the operator name forces PowerShell to make a case-sensitive comparison. The following statement will return false:
'Trees' -ceq 'trees'
In addition to this the case-sensitive modifier, PowerShell also has an explicit case-insensitive modifier:
'Trees' -ieq 'trees'
However, as case insensitive comparison is the default, it is extremely rare to see examples of the i modifier.
These behavior modifiers can be applied to all of the comparison operators.