We have honed travertine in two bathrooms and love them. I just mop and swiffer like tile. I sealed one with color enhancer (darkened it a little bit) and one natural. Ours is not finished or shiny. Very neutral. Out neighbors have there ole tire living space done in it with no problems. It can stain I am told but we have had no issues and we have had it in for about 6 years.

I've heard from several owners that it can chip easily? Even in areas where there isn't any traffic?

Get the tumbled type. Looks great for years. Love it.

Have had it in our kitchen for 15 years with no problems.

We've had a customer that put this in her beach home and is still in love with them. They are so much easier to maintain, as well..you could even use bleach in cleaning, and they'll only form a nice patina over time!

Is there a maintenance difference between honed and filled and/or tumbled?

There is not a maintenance difference. When you buy tumbled the holes are filled with grout when you grout it and both types are sealed after installation. The difference is really in the look you want. The honed and filled normally has a straight edge which gives you a smoother, more contemporary feel. The tumbled gives you a bit more rustic look. Hope this helps!