They are both safe to delete. There is configuration somewhere, possibly
in WeBWorK/Debug.pm which decides whether or not to record debug information on a regular basis. I suspect you've had that turned off for some time.
The timing info log can be useful -- I use it to see how the servers are doing under load sometimes -- but there is no reason to keep it long term unless you want to compare response times for each problem now vs. a few years ago. :-)
Is there more about the timing log and how to use it beyond what I found at http://webwork.maa.org/wiki/WeBWorK_performance ? I'd like to understand that better. (Maybe what is there is enough if I study it more.)
We do experience issues sometimes with slow performance, and I'd like to know better what to look into when such things arise.
I deleted all lines from the timing log from before September 2016. It had stuff going back to 2013. This dropped the timing log from over 3GB to under 2GB. (I think my timing log may be heavier with more recent entries owing to both an expansion of regular WeBWorK use, plus use by our PreTeXt books.) I'll make it an annual summer task to cull anything older than two years now.