Right now I have a Boss ds-1, not amazed with it, but it was cheap, and I don't hate it. I've been hearing some really great things about Big Muffs. I'm thinking about upgrading but I wanted some opinions first. And also please tell me the difference in sound between the American and the USSR.
the DS-1 is distortin, a big muff is fuzz

different effects.. kinda similiar, bit different.

go to a GC and try one out.
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^What he said. Having tried both though, the DS-1 is an 80's-ish gain(makes sense since it came out in 78'), the Muff is more a late 60's/70's fuzztone. Personally I think the muff is better, but that's all opinion.

As for USSR-vs-USA muffs, the USA has a sharper tone, and is a bit larger. The USSR is somewhat smaller, is much more simplistic-looking, confusingly has "CE" across from "Made In Russia", doesn't have a power jack(ie, batteries only), has an easier to open battery compartment as consequence of that, and has a slightly smoother tone.

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The russian muff has a darker tone than the american. So if you're doing more sabbath type stuff go with the russian, for more zepppelin/santana/stones stuff go with the US one.
I have the little big muff and its a great fuzz pedal for riffs and esp soloing but it can get muddy quick, even w/ power chord stuff
i was never impressed with the DS-1 myself, but then you get what you paid for, and you paid for boss's mildest distortion.
i also personally don't like fuzz effects, so i stayed away from the metal muff the store clerk tried to show me back when i bought my last distortion pedal.
Try going into a store and giving the boss md-2 a try (boss's best distrotion imo) also, try any tube distortions available, such as the tonebone and the satchurator.
And while you're at it try a few overdrive, just in case the tone you're after is up another tree then what you're barking.