True Travertine is more expensive typically that bluestone,clay brick or concrete pavers. Make sure you are actually getting true Travertine and not something like Jerusalem Limestone for example (which is a softer stone). Also, you can't use the same thickness outside as you would use and pay for inside. Typically, the material you would use inside in 1/2" or less in thickness, outside that would crack/break if something fell on it, if you used it as a tread for example, a person over 200 pounds may break the edge off. Also, may fracture from freeze thaw.

The Travertine we used on this project was around 14,000 PSI (pounds per square inch), very dense/heavy stone and 4" thick on a dry base for the pool deck. All the Travertine comes in square pieces and to make it irregular would be a very expensive and time intensive process, along with a great deal of waste and potential of not breaking the way you want.

It is tolerant to freeze thaw with greater thicknesses, but we have found that when you use this stone in thinner and smaller pieces it can break from crystallization. The stone wicks the salts from base stones and or concrete underneath and the crystals are sometimes denser that the stone itself (and can fracture).

I'm not a big fan of stamped concrete, looks commercial to me and I am a bit of a purists. I just like natural materials over man made protects, but that doesn't mean you shouldn't consider it. The main reason we went with Travertine here is that it doesn't get hot (we had no shade from the sun).

I hope this helps!

Howard