I don't know much about tumbled travertine, but can speak from the personal experience of having both in my parents' house.

The travertine they chose for a late '07 remodel now has crumbly holes where naturally weak spots of the stone simply caved in under foot traffic, deep scratches that wood furniture somehow made, and huge, deep ruts (some are like 4" or 6" long and 1" or 2" deep) from dining chairs getting carelessly pushed around. I would say the majority of the problems started showing up a year after installation, but the cave-in holes started appearing scant weeks after the floor went down.

The porcelain, meanwhile, likely has not a single dent or chip and has been installed for 2 or 3 times longer than the travertine.

I don't want to trash travertine on the basis of one bad experience, and I think it would perform MUCH better in a low traffic room that isn't constantly being stampeded by boys, but after seeing that... I'd certainly be too afraid to install travertine for myself, haha.

Either way they are COLD and HARD.

Tile flooring provides thermal mass, which is a good thing. It helps to stabilize room temperatures by storing and releasing heat. See the link for details.

Quality indoor footwear solves the hardness problem.

Here is a link that might be useful: Thermal Mass

Not sure if this would work for you but check out peacock pavers - concrete indoor/outdoor travertine look tiles. They do need to be sealed, apparently, but I am not sure if this is to give them the finish or for protection. They would be sturdier than travertine for sure.

Here is a link that might be useful: Peacock Pavers

Peacock Pavers have to be laid on slab. Don't know if that would be an issue for you. We looked into them during construction (are made in our state) and I loved the samples. Very disappointed when I found out we couldn't use on our main level (which is 2 stories off back of house/not on slab).

I have travertine flooring on our main level (kitchen, laundry, bathrooms, sunroom, etc). Sealed with Miracle Sealant 511. Dropped an oil based stain can lid upside down on the floor - wiped right up. It is hard, but I love it. We also did our lower level in travertine porcelain tiles, has rough edges so it's more realistic looking. I love it also. We've been in house just over 4 years, fyi.

Stone and tile flooring comes in all prices points and quality. The lesser quality stone is thinner, and more like swiss cheese. Look for better quality to avoid above posted problems. With tile, there are SO many manufacturers of tile - look around more. My parents used a tile inside and outside of their lake home. We were going to use tile on our three verandas but used stained concrete on the back two and flagstone on the front.

Good luck!

Thanks! I'll compare the porosity of tile candidates. I love walking across cool tile floors in summer. Supplemental radiant heat will counter winter chill. With respect to hardness, I will be so happy to leave behind my "softer" white oak floor, which requires constant upkeep. I'll check out the Miracle Sealant 511. (I just found out that 1 part bleach to 10 parts water lifts red wine stains, which is good; we've been joking about hiring Patinas-R-Us to break in the marble slabs by dousing them with Bordeaux.) We will have slab for terraces but none inside so Peacock Pavers wouldn't work.

Follow-up: Checked out Miracle 511 H2O and Dry Heat 40SK, the latter sealant supposedly holding up for fifteen years. These appear to be the best choices for people who do not have chemical sensitivities, as I do. Specification sheets indicate they are horribly toxic during application. Any volatiles released long term? Has anyone used the AFM SafeCoat sealers? Nonhazardous, nonflammable, no formaldehyde; but do they work?