Street Photography is a genre of photography that I've grown into and come to love. And like all styles it has its challenges to overcome in learning the craft. Or at least to produce images that stand out and tell a story, or even someday become an iconic image. May someday with that last comment, I don't think I've got anything close to that yet.
But what about the common question? Well, I often get asked what camera should I use and what lens do I choose? My answer to that is always one that you are comfortable with, that you know inside out and can use it without thinking. If you're not comfortable with it, then you'll miss the shots as you try to work out what to do. You'll look out of place and uncomfortable and thus stand out more, which is the last thing you want.
So if it is an SLR, a Fuji, a Leica Rangefinder or a point and shoot - use it. You'll get better images than picking up the latest "best thing since sliced bread" camera for Street Photography.
What do I use? I have two setups that I like to use -
1) Canon 5d Mk III with a 24-70mm F2.8 L series.
For some, this will be a bit of a beast. You will stand out a lot more than using a smaller body/camera and lens combination but for me, it is a lovely bit of kit to use. I can trust it when it comes to using higher ISOs. I know it will focus quickly and I know I'll get very good images to work with.
The grip also works well for when I use the "shoot from the hip" method to get images. It takes a little practice and there will be rejects but I trust it.
2) Olympus O-MD E-M5 Mk II with a 12-40 mm lens
The little Oly is a sweet bit of kit. It isn't as heavy for walking around the streets all day it is less of a strain to carry. With the flip up a screen with touch focus, you can stand in the middle of a crowd and take pictures without them knowing. If they do notice, it will be that you're looking at the back or be playing with settings. Add to that the silent mode and you'll not be heard either.
I find the images are noise at higher ISO settings than the Canon but still very much usable.
The main problem I had was with the grip being so small which made it difficult to use my "shoot from the hip" method. I adapted and managed to get good results from it too.
However, battery life is shocking when compared to the Canon so make sure you've plenty of charged batteries with you. I've added the additional battery grip to my setup which dramatically improves the situation and resolve the problem I had with the small grip.
All in all, the Oly is mo got to camera for street. Especially if it involves travel.
I hope that helps to answer the question. Well not really, but I don't think there is a correct answer.