There are tons of tubescreamer variants out there including many of the Maxon stuff. Maxon, if I'm not mistaken, was actually the original producer of the "808" pedal that we know today. Either way, they are both killer pedals. I own the Ibanez 808RI and am perfectly happy with it. The OCD and Fat Boost are VERY different pedals with a whole lot less of that classic midrange hump. The dreaded hump that all the modders seem to be trying to eliminate is (to me) what makes it a magical companion to the midrange-lacking amps such as the older Fenders/Marshalls. Here are some budget suggestions that I'd like to recommend:
BBE Green Screamer: very good tubescreamer clone that can be had on the cheap. They are well made, low noise, and true bypass (something that even the original didn't have)
Visual Sound Route 66: Cool OD with bonus compressor if you dig that kind of thing
Fulltone Fulldrive 2: THIS. My all time favorite TS derived pedal (besides the real mccoy of course) You get an extremely tweakable yet accurate version of the 808 with the bonus of a very good sounding gain boost. It's my desert island OD pedal!
Ibanez TS9- it takes audiophile ears to hear the major differences but I've owned them both...the TS9 is a little brighter and more aggressive? PERFECT for hard rock/metal guys. It is a great blues pedal too, but the 808 just has a little more of that smokey midrange that makes the amp more "chewy" if that makes sense. You are really splitting hairs here and you can nearly buy 2 TS9s for 1 808 so it's a really good buy.
Lastly, being a DSL100 devotee I can give you some JB tips for that particular amp. I like the green channel (clean w/ gain boost engaged), deep switch OFF, Mid shift OFF (meaning the "more mids" setting) treble 4-5, mids 6-7, bass 6-7, presence 2-3, volume 7, gain 6-7, then start with all the tubescreamer knobs at noon. If you are happy there then have fun but depending on your rig/guitar/strings you may want to tweak. I like my tone knob on the TS at about 10 oclock, the volume 1 oclock and gain 10-11 oclock. All knobs at noon is just a great starting point then tweak to taste!
'67 and '74 Fender Twin Reverbs, '74 Marshall 1987 lead mkII, Metro Superlead 100. Pedals from TC Electronic, Ibanez, Dunlop, BK Butler, Electro-Harmonix, Fulltone, Maestro/Gibson, Loopmaster switching, VoodooLab, Boss. Gibson and Fender guitars, Dimarzio pickups.