Let me state clearly that i'm no pro on concrete vs porcelain, but as a layman here are my thoughts, and let my thoughts please bump up your question so the pro's may see it and correct me whereever necessary :
1) Concrete is porous so it shall absorb/soak up such nasties, including water and humidity
2) As i understand it, porcelain shall NOT do what concrete does in step #1 above

3A) Does #1 & #2 above say that porcelain is stain RESISTANT ? Maybe
3B) Does it say that porcelain is stain PROOF ? Absolutely not

I've used both and because concrete will still be porous even after staining, with the issue of dog urine, I think the porcelain tiles would better protect your floors and not absorb any 'accidents'. Porcelain is not as porous, you'd need to seal the grout lines. With our dogs inside in the past, porcelain has been very easy to keep up & is really durable.

I really need to chime in on this. As the prior people have said, concrete is porous and can be stained if not sealed properly and the seal maintained properly. porcelain tile is a completely nonporous product. i have yet to have any customer or peer contact me and have a stain issue with there porcelain tile.. The one thing i would recommend is to use an epoxy grout. After the cure time, the only way to stain-it is to actually mark on it with a permanent marker. the marker can be cleaned up wit acetone.

Thank you for the responses:) Going with the porcelain tile.