Bamboo floors with cats and dogs
This is really about your expectations of the flooring.  If you are more worried about looks then you need to go with a solid hardwood.  Bamboo is a very hard wood and will last many pets - when we are talking about surface damage.  

However scratching will eventually breach the stain/poly finish - and then when they pee/poop that will get in the wood and it is basically never come out.  So this depends how well you upkeep the floors and how many accidents you have.  The "look" of the floor will be dependent on the wood rating and bamboo is very hard (oak would be fine too), the grain of the wood (wood with more character hides things better and flat woods show), and the color - a light color will hide scratches.

Your other option is pure vinyl/rubber laminates.  Here is something that I have installed - also Home Depot has a line of planking (and some look like porcelain tile) that I have used.  Both were great - installed easy and pure rubber.  Have used them in many many basements.  This won't give you the exact feel of hardwood but they look great and can be FULLY cleaned.  

So it really comes down to the upkeep you want to do, how truly clean you want everything, and the look/style you are going for.