It boils down to what you want to do with the travel pictures. If posting on a travel forum, Facebook, or Instagram a iPhone or any Smart Phone meets that challenge. However, if you want to blow up a shot to a 24" x 36" and print it on metal – not sure a handheld phone is the instrument you want to use.
Like some other above I am primarily a Canon guy, albeit for underwater I like my little Olympus point and shoot. I loved that Olympus to death, but the last trip to the USVI I saw the dreaded bubble come from the camera. I am in the market for another durable underwater point and shoot.
When I travel I always carry my Canon G15, which is large for a point and shoot but still easily fits in a pocket or nice belt carrier like Pauline showed, and it has a WONDERFUL piece of glass. I did not upgrade to the G16, or the one that was just released, because I felt that that the G16 added to many bells and whistles at the cost of durability and control. The zeal for camera companies (computer companies also) to make everything easier for the user “usually” comes at the cost. In the case of cameras it is usually the sensor, durability of the camera, or the piece glass in the lens. I never care about megapixels – no a major factor in quality.
My big camera body is a Canon EOS-50D. Yep another old one, but oh what a body! Single processor, but the sensor and noise specs exceeded anything out there at the time in the price range. Canon, fell into the trap to make a more competitive camera body with new “features” at a lower price, and moved away from the EOS 50D. What followed were the 60D and the 70D, and IMHO it lowered the family blood line considerably, which began with the 40D. My son has the Canon 7D which is a big step back in right direction, but to me it is not as balanced and clumsy and my old 50D still the one for me. I will just keep getting my 50D cleaned every couple years until I can afford a MK series body. However, then I would probably be scared to take on a trip due the investment. Which goes back to the original question of what camera do you travel with? To me it is not the question of camera, but what lens(es) do I take for the big camera, the G15 for sure, and waterproof if headed to the islands.
In the old days… the rule of the thumb when buying a stereo system was to put your money into the Cartridge (Needle) and the Speakers. Digital cameras are the same – It is the piece of Glass and the Sensor. A phone cannot offer either at high level of quality at this time.
I will say again, it is what do you want to do with the picture and how much time and effort you want to learn on operation of the equipment. Of course, the other factor I always consider is what I will be doing on vacation. If I was pilgrim walking the entire Camino de Santiago and had to carry everything, my Canon G15 would be all the extra weight I would want… In fact the little Olympus Underwater Point Shoot just may be all that is needed.
So here is three shots – with my three cameras. All have been compressed to a 1280 by X for upload.
Canon EOS-50D
Canon G15
My old Olympus Underwater - May you rest in peace
Not sure there is that big of a difference in the post, but ohhhhhhhhhh when you print them.
I would add a couple hints on things that have burned me when traveling with multiple cameras which now I always do: a) Take the time to sync the clocks on all cameras. It will make your life a lot easier sorting for a show later on. b) Always leave all cameras in AUTO so you are ready in instant. Best to get the picture if it happens fast than miss it trying to set for proper aperture or speed. Then take the time to set up the shot with your artistic choices.
Personally when it comes to smart phones, I wish the phone manufactures would use the available space in those amazing little boxes to improve the TRANSMITTER and the RECIEVER - We have reached a point that Smart Phones are everything, but a phone. But of course I live in a very rural location and signal strength is minimal.
. Rome Addict is exactly right, “The best camera is the one you have with you”, and that is why my G15 almost goes everywhere. The crop duster picture above I was driving down a country road and saw it coming streaking across a field at me – I jumped out of my car and SNAP. I am not sure a phone would have stopped the plane in flight. 
