Are these ancient machines actually better than anything I'd buy new?

Kept a gold set like that in my last place for six years and finally sold them working when we moved. The washer was a belt-drive Whirlpool-built machine from the mid 70s and the only thing it ever needed from me was a new inlet valve and a belt, both cheap and both fixable in an afternoon with basic hand tools. Everything in those machines is mechanical. A timer, a motor, a water pump, a couple of solenoids. When something quits, it's usually a five or ten dollar part and a YouTube video. Compare that to a modern unit where a failed control board can run half the cost of a new machine, and the math gets pretty clear.

On the utility worry, you're overthinking it a bit. An old top-loader does use more water per load than a modern HE machine, maybe double, but it's not some hidden drain on your bill. If it bothers you, fill a bucket and check the flow, or just watch a cycle and see how it behaves. The dryer is where old machines actually do fine, because a dryer is just a drum, a heating element, and a blower. There's not much efficiency to be had either way. What I'd actually do in your position is run them until something breaks. Keep them while the laundry room is fresh and empty, get familiar with them, and if one dies a year from now you can replace it then without any pressure. The failure mode on a washer is usually just stopping, not flooding. If the hoses are original though, swap those for stainless braided ones right away regardless. That's cheap insurance and old rubber hoses are the one weak point. The one real maintenance item: pull the dryer away from the wall once a year and clear the vent run and the lint trap housing. Lint buildup is what kills those old dryers, not age. As for built like tanks, yeah, that's not a myth. Those direct drive washers ran twenty and thirty years routinely, and parts are still easy to find because there were millions of them made. You'd be replacing a known-good machine with an unknown one, and modern budget machines don't have a great track record on longevity. If the dial still clicks through its cycle and the spin gets the clothes reasonably damp rather than soaked, you've got buried treasure. Leave it alone.

One thing I'd add before deciding is to level both machines properly, because a 70s washer that's sat in one spot for decades has often settled unevenly and a machine that old walking across the floor is what actually damages things, not the machine itself. Also check underneath the washer for a small dark oil spot on the floor, since a seeping transmission seal is about the only fault on those that isn't worth fixing. If the floor's dry and it doesn't thump on the spin cycle, I'd run it exactly as the previous poster described.

We got a harvest gold set with our place too, and about a year in the dryer started making this horrible scraping noise. Turned out the felt drum glides were worn down to nothing. A putty knife popped the top clips on that old machine in two seconds flat, and honestly that little moment is what sold me on the whole era, no disassembly nightmare, everythign just unclips. A couple dollars of felt strip and it ran quiet again. So if yours ever starts thumping or screeching, don't assume it's on its way out, that noise is usally just a wear part doing its job.

We swapped ours when we moved in because the wife wanted matching new stuff, and honestly that's my one regret from the whole reno. The old washer went to a guy off marketplace who fixes them up and resells, he paid me fifty bucks and hauled it himself. The new set needed a service call within two years. Now when something acts up I open it up myself first, the old ones were just friendlier that way.