In Photoshop, it would be easier like Joe said. (For most probably)
If you use Photoshop, start with a high contrast image, the higher contrast helps bring out the type of highlights and shadows you'd need.
Play around with Threshold, it's a filter that makes an image a black and white SUPER high contrast image.
That's similar to what they did to create the Big Lewbowski image on the t-shirt.
That kind'a stuff is really easy to do too, but, you have to know what the program does, otherwise you'll spend a lot of frustrated time.
They then vectorize it, which is easier to do too, but again, it's all in what you know.
I'd definitely advise to go to YouTube, or do a search in Google for Threshold+photoshop, (the + sign searches within a search) and see what you turn up, there's PLENTY out there in the way of free tutorials.
There is also a website that lets you turn any image into a .bitmap or .png Threshold image for free, I don't remember the name, but maybe someone here will.
You'd have a little more control using Photoshop though, but not by a lot.