The only 7013 I have ever seen wasnt very good. Basically a 7013 should be the same as a 6013 in terms of welding characteristics. The 70 part denotes a higher tensile strength than the 60. The reason for this is that the core wire had higher carbon (in the one I know about) which isnt good for the welding. High (er) carbon core wire is usually associated with poor quality steel. When the steel maker removes Carbon he also removes impurities at the same time.
I suppose if your doing garden gates they should be OK.
i had ago tonight on the 7013s they seem to penetrate a bit more than the 60 13s and seem stronger as well. i think they need drying a bit too as they fizz and stick like hell, time for the oven.