There are all of these types of electrodes produced only to confuse non welders. At least thats what some of the maintenance personnel I have had working for me at one time or another seem to think. Welding rod like most other tools are made to do a specific job in most cases. The numbering sequence tells the operator what the rod is intended to be used for. You can do a search on the internet and find the numbering key that explains what each digit means. From this information you can then choose the proper welding rod for the job.
One is no better then the other depending on the application. The E6013 is just a more versatile rod. If the choice was to purchase and stock one over the other then the 6013 is my choice. If buying for a specific job and the 6010 will do then use it. It can be a little less costly. Also for beginners the 6010 easier to learn with.
__________________
Life is not a journey to the grave with the intention of arriving in a pretty, pristine body but rather to come sliding in sideways, all used up and exclaiming, "Wow, what a ride!"