bash script: how to diff two files after stripping prefix from each line?

I have two log files. Each line is formatted as follows:

<timestamp><rest of line>

with this timestamp format:

2015-10-06 04:35:55.909 REST OF LINE

I need to diff the two files modulo the timestamps, i.e. I need to compare lines of the two files without their timestamps. What linux tools should I use?

I am on a RedHat 6 machine running bash if it makes a difference