Honestly, if it’s just for posterity and not for some fancy artistic shots an iPhone is plenty. The one drawback is that phone battery drains fast during travel with google maps, research and general planning. But you can get a power bank and then you’re good to go.
Lugging around a dslr is tedious so I feel you really got to be into it for it to be worth the effort. You’re always paranoid of getting it stolen, it’s heavy, and it’s an extra device to think about charging, dumping and backing up the footage etc.
A lot of people opt for the action cam like a go pro, but personally I dislike the wide angle look, and if you really want to make the most of it you’re also stuck with 5000 accessories.
There is also a middle ground with small pocket cameras / compact mirrorless cameras that I like if you have a couple hundreds to spare. You get a dedicated camera with a longer lasting battery, quality can be a bit better than your phone (zoom, low light capability), and you look less like a target for theives.
In the end it all comes down to how much effort you’re willing to put in for “the shot”. I’ve met many people in my travels that buy a big dslr that they end up leaving at home 95% of the time because it’s a pain to carry around.