A few years, been at it since I was 14 and I turn 40 in a month or so. Landscape architecture degree, minor in horticulture. Sold my first project when I was 17. Whether it's a $500 project or $500,000 project it's do it right or not at all.
I am biased to pavers, like concrete guys are bias to concrete. Sorry if this offends a concrete contractor. More and more the attitude is not if it will crack but how soon. Frankly I don't know how you can throw down a couple inches of gravel, pack it for a minute, pour mud, and expect it not to crack. Control joints are part of the key.
Stamped concrete. Yes it will crack. The other downfall is that it is slicker than snot. Snow on it is the worst. Ice is safer. Water not too bad but still slick. Don't let em blow smoke there is a product to make it not so slippery.
DIY - most stamped here runs around 7-10$ a sq ft. Depending on access, pattern, ect. Pavers, just the pavers, 3-7$ per sq ft if you don't pick out something crazy expensive. So buy the time you rent equipment, gravel, ect. You would be pretty close. If pricing there is about the same.
I would guess a small patio that size is about 40 hr project maybe a tick more depending on shape, cutting, access, amount of cut and fill ...... You get the picture. Don't expect you and 3 buddies to have it done in a day though. That's 40 hrs for someone that does it everyday.
If you go the paver route. Fill the paver joints with poly sand. There is about 4 different brands. I can discuss that further if you go the paver route.
Don't buy pavers from a big box store. They are considerably less dense. Much softer. When you get done and pack the pavers in, you will end up with a bunch of broken pavers. Try to find a landscape wholesaler.
Ooooof I can keep going if needed.