I own two ts-808 style pedals - a BYOC overdrive 1 and a Digitech Bad Monkey. I like and use both of them quite a bit. Here is a side by side comparison.
I find the BYOC to have better dirt, a little more natural and less "pedal" like. It also does a much better clean boost. The Bad Monkey has some nice EQ options though with dedicated Bass and Treble sculpters. If I want something really fat with single coils this is the pedal I go for. There's a reason the tubescreamer is so popular - it sounds great!