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If you want to fold your bike several times a day, with a hard time constraint (i.e. your commuter train is about to depart) and a tight space constraint (the crowdedness of your train), a Brompton is what you want. I commute by train and I own one for this purpose!
If you're taking a leisurely touring holiday, you can afford to take a bit longer over the fold, and for the folded bike to be a bit bigger. I wouldn't take the Brompton touring: it can be done at a pinch, but it isn't the proper tool for the job.
^^This seems to hit all the right points spot on.
I must be one of the very few on here who don't have a good word to say for the Brompton. I have tried it but its only merit for me is for commuters getting on and off public transport in a hurry - a bike for folding and carrying first and riding second. Caveat, all the people who get on with riding Bromptons seem to be smaller than me! They can go long distances if you happen to be the right fit, several on LEL this year, of which at least a couple got home fairly comfortably. I would hesitate on off-road. Dry canal paths and similar perhaps.
I have an italian clone of a Dahon, 20" wheels. It is fine doing distance, it will carry a full camping load (with attention to weight and loading). It fits in a bag for going on buses but you would not want to carry it very far and it is very easy to scuff the bag on the floor. (I needed to put it in a bag to go on Stagecoach buses this summer; I am now thinking about putting it on a pair of wheels for moving around, the bike bagged plus loaded panniers plus rackbag on a shoulder strap was not easy for climbing onto - and off - the bus). It needs good tyres to be fun to ride but it can handle off-road (although I haven't tried that with a full camping load). A proper tern or Dahon would be better and probably wouldn't have the rubber shock absorber in the steering that makes it a right pig with a front load!
The best advice would be to try them all, carrying folded and riding and looking at how you can carry the luggage that you need. Tern do a front lo-loader, the Spartan IIRC which will take small panniers (I have it adapted to take big ones!), Brompton have the block and front bag. If you want to use buses and feel right on a Brompton it is probably the best choice for carrying. If you don't feel comfortable on one then the portability becomes secondary. 20" wheels do roll better, 24" better still. An Airnimal with 24" wheels will pack not much bigger than my 20" wheeled machine, although with a bit more work. A Dahon may be smaller folded than mine.
Check whether the buses that you would want to use require bikes bagged or not.
ETA For the sort of touring you are talking about, on my sort of folder I would not want to take the panniers. A rackbag would be easier. I have an 11l Vaude which would probably be sufficient although they exist from various makers up to 40l (a humongous great lump which I would not want!). Something about 16-20l might be a better option. Check that the rack is big enough! On a Brompton the choice is much easier (but more expensive).
