Uh boy. We've been down the road of cedar vs other wood many times, and I keep coming back to cedar because I like it, but it is pricey.
Around here you can expect to pay about 50% extra to use cedar over PT wood on your projects. And it looks 100% better, but functionally (despite what others say) I find little benefit to it over other PT outside.
(My super-pretty cedar garbage shed is documented here:
http://frosthaus.blogspot.ca/2014/05/the-trash-cabana.html)
If you want to save some cash, you can frame your project in whatever wood is cheaper (PT) and then clad the exterior in cedar. Use PT for anything that touches the ground. This is pretty common. Just be sure to use ACQ friendly fasteners.
Finally, if you don't maintain the wood, everything will grey out over time, and after about 4 summers, teh only difference between the cedar and PT will be the grain. If you are staining the wood, definitely go with the cedar and it will look and last better.