I've been looking at tires and one website says the foldable tire is superior in all ways except price. Is there any downside to a foldable tire vs. a wire bead?

Like, durability, ease of install, flat protection, etc....

thanks

All other things being equal, the plus is a lighter weight for the folding tire and the minus is a higher price.

It all depends on the size... Folding flat Kevlar bead tires make great 3rd tires.
for spares, But a 27" /700c tire can be shall we say Bandsaw blade like reduced in diameter
for travel as well it rolls up in 3rds, by forming ins figure 8 and then into 3 rings.

light skin wall not HD tires .. Kevlar bead or there is A Kevlar puncture protective band
to reduce puncture vulnerability.

have specific tires in mind?

We use Kevlar bead 28mm Conti GP 4 Seasons on our tandem. We don't generally carry a spare tire onboard, although the one time we had a spare I needed one - go figure. These tires have proven very easy to mount and dismount; they can be mounted without tools and if I worked at it a bit I could dismount without tools.

I think there is anecdotal evidence that says Kevlar beads expand less at high temperatures something that's a bit more important for a tandem.

My experience also suggests that you will have different results with different wheels. Sun rims deal better with kevlar, IME, than wire bead. (The DS-2 rim I had in 2005 wouldn't even TAKE a wire bead!) I attribute that to the shallower rim bed in the Sun rims.

When you're doing a tubeless conversion, wire beads hold their shape a bit better at first; I've taken to putting my kevlar-beaded tires on spare hoops and letting them 'settle'.

This works well once you figure it out, but I can't think of a way to explain it that's clearer than this. You hold the tire in two hands, palms up, and sort of rotate and twist...you'll work it out. They'll fold down small enough to fit on a rear rack or into a small pack, but not a jersey pocket.
Another possible minor problem with Kevlar beads is that they can be finicky to mount. The bead is floppier than wire, so check to see that it's seated all the way around.

Nothing in mind yet. Was wanting to get Bontragers since I have the Specials now and they have done well. New specials are $25 each and what I like to spend. Not yet sure if they're available in folding kevlar, but I'd bet they would be expensive to ship if they're wire beaded. I'd consider Michelins and Continentals since they are name brand, but do not want colored tires since I read here of some times separating and they look foolish to me anyhow. I'm really focused on FLAT PREVENTION. All else (weight, grip, treadwear, RR) being secondary concerns.

I never ride in the wet/rain since I have no fenders. Although it is for a road bike, I usually stay on the shoulder where there is lots of pea gravel, but I do take it down a grassy/hard pack trail once in a while, but not enough to get a treaded tire. I do take it easy since harming the wheels is possible (or so I've read on the Trek webpage).

Folding tyres are lighter and tend to be easier to mount and dismount.

And when you buy a folding tyre you are usually buying a better tyre as folding tyres tend to sit at the top of the food chain.

Maybe you are simply looking for a simple answer. If you are not concerned about weight then about the only real difference between a folding tire and a non folding tire will be price. A folding Gator Skin will last about as long as a wire Gator Skin but the folder will be just about twice as much. About $35.00 to $38.00 for the wire bead and $54.00 to $65.00 for the folder. They both will last about the same amount of time. The folder will usually be a few grams lighter and easier to store if you need to store one. The folder will fit in a back pack or even a camel-back.

unless you are racing at a lever where the weight difference means first or second place or you ride 100+ miles on a regular basis and need to carry a spare get the wire bead