I am migrating to a new server so wanted to transfer couple of websites, one website has a large error log file, it is taking too much time to download, is it important to transfer the log file or i can transfer all other files and leave this?
Just leave that for the time being. That is not needed. After transferring if you decide to keep a backup then just download the error log to your computer instead.
No, error_log is not essential. It just saves the error log. It does not have anything necessary. You can just leave it.