I have a Brompton and I freaking love it. You look ridiculous riding it, like a circus bear, but who cares?? I fully embrace the ridiculousness. I use it a lot for multimodal commutes, and it’s also very useful at work when I need to move vehicles around, as it allows me to do by myself what would otherwise take two people and another car. I’ve taken it to Portland OR twice and rode it right out of the airport both times. First time I carried it to the gate (it fits in X-ray machines) and gate-checked it, the second time I carried it on and fit in the overhead bin (fits there, too, in the larger ones.) When I arrived I carried it off, unfolded it, rode it (slowly through the terminal, out of the airport and to the bike path along the Columbia and right to where we were staying. And I had a big-ass smile on my face the whole time. When I need to go to the grocery store, I just half-fold it and wheel it through the store like a grocery cart, putting my shopping in the bag. It’s designed to fold into the smallest possible package as quickly as possible and it’s absolutely brilliant at this. It also continually get lots of attention. The security guard in the lobby of my office has a ritual with me where she unlocks and holds the stairwell door for me while she watches me fold it because she finds it so entertaining.
Before I got the Brompton, I had a Bike Friday for a couple of years. In 2016, my mom rented an old farmhouse in the Dordogne for a month (it had been a dream of hers for years) and I went there for a week. There was no way I was going to go to the Dordogne for a week without bringing a bike, but briniging one of my normal bikes seemed like too much of a hassle. (I didn’t learn until after the fact that I could have done it for an entirely reasonable amount of hassle), so I bought a Bike Friday with its travel suitcase-trailer off of an acquaintance from a bike list I’m on. Picked it up when I was in New York for a weekend and took it home as a checked bag. It came with a modified Samsonite hard shell suitcase that would turn into a trailer so you could pick it up from baggage claim, assemble it, add the wheels and hitch to the case, hook it up, put your bag in the case and ride away. I was dying to do this but ended up doing it first in the Brompton. Once I got the Brompton I had no real need for it any more, so I eventually sold it.
Between the two, given that the OP was looking for a “good-riding road bike that I can take on trips”, the Bike Friday is hands down the better choice. The Brompton is designed as a commuter bike, designed to fold down as quickly as possible into the smallest possible package, and it does his brilliantly (and I never stop getting reactions from people when I am out and about with mine). A Bike Friday is designed to ride like a normal bike while disassembling into a suitcase that you can take on a plane or put in a car trunk, and it does a great job at this. My normal road bike is a Vendetta custom and it wasn’t as nice as that (it’s a joy to ride, so that’s a tall order), but I can genuinely say that it really does ride like a normal bike and it was at least, say, 90% as fun and a ton less hassle than packing a full-size bike into a box.