Id probably say grade 43 High test. Grade 30 proof coil is weakest grade you can buy and id compare that to about a grade 2 bolt to give you an idea if my hunch is right. This is the cheapest but weakest and will wear more, stretch easier and damage easier. This is usually silver in color.
The grade 43 High test is about 50% stronger and referred as logging chain sometimes or binder chain. This tends to come black in color 3900 lbs. for 5/16 and 5400lbs. for 3/8.
I hear you ARROW, I found a 1/4" 20 foot chain when I moved in here and decided to give it a try. I pulled a couple good sized logs with it. I doubled it up and hooked it to a 20" diameter Hickory tree that had fallen could hardly move it but the chain held up, and that was with the 6500lb Excavator, I suspecting that little chains probably grade 70 or even 80 to hold up like that!
Then there is transport grade 70 which is 20% stronger and most expensive. This is more of an alloy chain and ratings are 4700 lbs. for 5/16 and 6600lbs. for 3/8. So the choice is yours.
There are higher grade chains but you don't normally see them available in stores as the other grades are more common.
I have 3/8 grade 43 and 5/16 grade 70 for trailer and to use for other things like towing logs out, I tend to use 3/8 for this as it has more wear surface on the links and I believe its a little cheaper to replace too.
If you don't mind a bulky chain go with the 3/8 G43, but if you want something easier to handle and get under a log go 5/16 G70.
Like CAL G said you probably wont be able to break it if your running a 30-40 horse or smaller, unless your running over a sharp edge and damage the links.