I run a small photography company with 9 shooters we've got pretty much every sort of body for different things, I use a 1DX when we have to shoot festivals/big acts, Rihanna, Aerosmith, big names, that kinda stuff. for street stuff the 85 1.2 isn't as sharp as the 1.8 for a lot of practical applications and also heavy. I use both lenses btw, for portraiture it's a great lens, it produces some results you can't get from any other lens. I don't use it half as much as I used to, but it's still a really bloody good lens.
The best street set ups are usually compact if I'm street shooting I prefer the 5D/6D and the 28mm 1.8, 40mm 2.8, 50 1.4/1.8 and the 85mm 1.8. I usually tape mine up, and usually take my Mark III. Usually taped up, if I need a flash a 280EX is enough.
Anything with a red ring draws attention, I also dress in dark clothes, and never take a camera bag, usually just a shitty backpack with a camera bag insert.
I've had junkies try to mug me twice (I'm based in Sydney), I've been knocked around a few times, and had a guy punch me in the head leaving me bleeding, luckily the dude did nothing to my gear but that was whilst doing a job a few weeks ago at night. ~ I do a lot of event work though so it comes with the territory, we cater for a lot of clubs, bars, live music.
I'm making these points because whilst Sanj's point is right, that set up is technically superior, the 1DX is load, bulky and you can't force it under your jacket like a 5D with a 50mm.
Street for the most part is about really blending in. In some places you can get away with it, but I like the fact street work leaves expensive gear at home, and makes me move towards the bare essentials. A person raised it well before that nothing beats good composition no matter what camera you have, I think that's true, but good composition often requires better equipment to be able to make the shots in low light, if your max iso is 1600 then things can get a little tough.
Anyway that was my 2C