Can you provide some more info:
- Where is this? (closest metro is fine, looking for climate context)
- Will the stamped concrete option be a slab or also pavers?
- Topography (is this the top of the site slopes or bottom?)
- What is the intended use of the back yard?

Here's an older post describing the basic differences in paving materials: http://www.revolutionarygardens.com/your-patio-stone-pavers-concrete-or/

In a nutshell, your best quality, artistic stamped and colored concrete is going to be pretty close in price to your lowest-priced concrete pavers. So the advantage stamped concrete has is budget, plus it typically goes in quicker. It's typically not my first choice, though, because it can look cheap, concrete WILL crack (all we can do is try and control where), and if it's damaged there's no patch or repair that will make it look the way it did on day 1.

Your higher end pavers are solid, durable, and attractive, and any damage is easily repaired and generally not noticeable.

It's in Suwanee, GA

It's on flat back yard. We want to use it as just reg use of back yard.

That's a good review of the issue by Revolutionary Gardens.

One note: your area gets a fair amount of rain. I would encourage you to consider the implications of this change on your site drainage. And from what I can see your yard is lower than your neighbors on at least two sides, so you have the potential for water accumulating in your yard in a significant rain event.

Open soil (with or without vegetation) soaks up rain and lets it dissipate slowly, mostly down into the soils below. Pavers will reduce this effect and created more water on the surface looking to go somewhere. A concrete slab will stop the process entirely and all that water will go to the lowest surface point ("sheet draining").

To reduce the amount of sheet flow with pavers, you can use gravel layers under the pavers. You can also lay some drainage piping under the area draining to air at some other low point location or a site drainage system to help pull out water from problem areas (like along a building wall).

If you use a concrete slab to lay the pavers, or for stamped concrete, none of it will percolate and it will all sheet drain to that low point on the right. You'll want to do something there to deal with that site drainage flow.

Also, if you haven't done it already (I don't see evidence of it) it's good practice to have a sub-soil drainage pipe along the up hill side of the retaining walls. It can drain off to a site drainage system or out onto the lower level if you can tolerate seeing the holes in the wall (or hide them with landscaping).

GIred
Vhfgc

I would say pavers are your best option. Pavers are just the real deal. If you are looking for a lick and stick, fast and cheap then stamped would be an option. It also depends on what you like. Pavers are the cheapest form of pavement over time but one of the most expensive to be installed. They will save you tons of money over time if installed properly. Proper installation is going to be your challenge. Everybody from Sam to Jack say they can install pavers but a lot of contractors don't really have a clue on the proper procedures.