I've never owned a folding bike, but have ridden lots of other bikes (from cruisers to racers to all sorts of mountain bikes). Could someone who's spent time on a folding bike and a conventional road or mountain bike compare the riding experience (level of effort, speed, balance, etc). I'd consider getting a folding bike for international travel, but if they ride like a heavy beach cruiser I'd just as soon rent a conventional bike at my destination as I've done in the past.
You don't need to make any sacrifices with a Bike Friday. They're a very high quality bike, made-to-order in Eugene, OR. Mine rides virtually the same as my traditional bikes. It takes me 25 or 30 minutes to pack it into the suitcase, and the same amount of time to put if back together. It goes into an off-the-shelf hard-sided plastic suitcase. My current suitcase for it is made by American Tourister.
I've never had to pay any bike fees to an airline, which were often outrageously high. I have flown with it at least 30 times. So far, no damage. And it was made to fit me. The weight is about the same as my traditional touring bike or my old mountain bike. While mine is their touring model, Bike Friday has models more like a road bike, as well as like a mountain bike. They even have a tandem, which packs into 2 suitcases.
Personally, I would not rent a bike for any serious riding, esp. for a tour. I have learned the hard way that if the frame doesn't fit me, I can injure my knees easily.
Some cyclists say they find the steering "twitchy", whatever that means. I don't. I do find the steering a bit more precise than my other bikes. I prefer the precise steering because most of my riding is in urban & suburban areas with traffic. You can get virtually any components you want.
I toured on my Bike Friday in Colombia last year, which is a very mountainous country. I toured in France with a friend for our 60th birthdays. He also has a Bike Friday. He always followed the Tour de France and wanted to do one of the famous climbs of the Tour. I had previously biked up the Col du Tourmalet & Mont Ventoux on my BF with panniers. So with my friend, we climbed up Alpe d'Huez (the hardest of the 3). I've also used it to tour on the unpaved GAP Trail and C&O Canal towpath.
I've always been able to leave the empty suitcase in a hotel or with a friend while I toured, so that hasn't been an issue.