Color and strenght. One is usually available OTC, while the other is a prescription drug. Where I live, you need a prescription for 1%, while 2% is available OTC. The only reason is that 1% needs to be imported. It's ridiculous.
I used 1% for a couple of years then switched to the 2% after I realised you can get it on the NHS. Both seem to dry out the hair which for me at least, means it looks much thicker.