Is it safe to delete the content of ~/Library/Logs?
Yes, log files can be safely deleted. Next time a log file needs to be appended to and is missing, it will be created (don't delete the actual Logs folder itself though). Log files are always presumed transient. However, before you delete all your log files, it might be worth keeping the most recent content of the most important log files in case you need to troubleshoot any problems.