I'd say the tubescreamer is different. I have both of them.
The Ibanez tubescreamer TS9 is better for a warm bluesy sound. I usually use it for solos, but when you play chords with it it sounds a bit like The Hives ("Hate to say I told you so", e.g.). You can also activate the TS9 while you already are in the disto channel of the amp. Using both at the same time can sound quite metal.
The EHX Big Muff is better for an fender-like overdrive (an overdrive sounding like fender amps). I usually use it while playing chords to get a sound a bit like Green Day, but it can also sound jazzy for solos. Also good for metal when used with the right settings.
The choice is yours, it depends what wou want to play and it depends the sound you're searching for. If you have a lot of money, I'd suggest to buy both. Otherwise, try those two before you choose.
Anyway, you also have to know the tubescreamer TS9 (~155&euro
is much more expensive than the Big Muff (~80&euro