The SD-1 and Tube Screamer are very similar; basically the same circuit with slightly different component values. The SD-1 has three diodes in its "asymetrical" clipping section for a little rougher sound than the TS' 2-diode "symmetrical" clipping. These pedals are both overdrive circuits, with the clipping section in the negative feedback loop around an opamp stage. It's not hard to convert an SD-1 into any of a variety of Tube Screamers, though why anybody would want to is beyond me. (OK, yeah, I'm a fan of assymmetrical clipping.) The SD-1 sounds better from the get-go, and with a few mods, can become any n umber of brilliant overdrive pedals. Mote Allum's GT Mod kit is a good one that I've built. Brian Wampler published a DIY Eternity Mod a while back that's extensive but sounds great. There are lots of others on the web.
The DS-1 is a distortion pedal; its clipping section is completely different, cliupping the signal to ground after the opamp gain stage. So, you're not going to be able to modify a DS-1 into a TS. However, like the SD-1, there are tons of great DS-1 mods published on the web. The best-known is the Keeley SEM/Ultra mod, which Keeley will do for you, but it's also published for DIY. The Ultra is much better than a stock DS-1, but still not the best if you ask me.
I recently tried Brian Wampler's Vintage mod - also a pretty good DS-1. That pedal I just re-modded into something like Monte Allums' Recto Mod for the DS-1, which is perhaps the best I've heard.
Keep in mind that the DS-1 is a distortion pedal, and it's purpose is to add distortion and compression, so in genreal the DS-1 is not the best choice for adding clean boost. The SD-1 and TS are better at that. But... if you want more volume boost and dynamics out of a DS-1, look at mods that replace the clipping diodes with LEDs. LEDs clip at a higher voltage than regular diodes, and so allow more clean signal through before they start doing their dirt thang. Of the mods I've mentioned, the Wampler Vintage and Keeley SEM replace one clipping diode with an LED. The Keeley Ultra takes it a step further and replaces BOTH clipping diodes with LEDs, so that one probably has the most boost before distortion.
Your DS-1 can be made a lot better than it is, but it will never be a Tube Screamer. Get yourself an SD-1, too, and mod them. Both styles of pedals are worth having in your arsenal.