Batteries for solar application, why C10 only?
The C-Rating has to do with how fast you can discharge the battery.  C10 means that you will get the rated Ampere hour capacity if you discharge the battery completely in 10 hours.  

This site has an explanation of the C-rating system and what it means.  In short, the faster you discharge a battery (the higher the load is that you put on it) the less energy you will get out of it.  Take a battery rated for 100Ah C10.  If you put a load on it such that is discharged to its limit in 10 hours (10 Amps for 10 hours,) you will get the rated 100Ah out of it.  If you put a smaller load on it (say, 5 Amperes,) then you will get more energy out of it (perhaps 120Ah.)  The exact relationship between C rating and actual discharged energy depends on the battery chemistry and structure.

You use the C-Rating to match your battery to your expected load.  A 100Ah battery rated C40 wouldn't be much good if you need to draw 10 Amps for 10 hours - it won't deliver that much energy that fast.

Presumably you would want to use  C10 instead of a C20 because it can deliver more of its energy in a short time - it is better for heavy loads.