For myself the parks, I carry either a high quality compact: Nikon Coolpix P7800 or A (or both), or I jump right to a ILC. On my next trip, I'll probably pack my Df and a few manual focus prime lenses and have fun with those, but realistically you don't need full frame in Disney: APS-C is fine, you'll so rarely need even ISO6400 that you're better off with the smaller APS-C lenses. Without the larger sensors, you can't get either the dynamic range or high ISO performance in your phone. And if I want to share or post something quickly, I transfer it to my phone over Bluetooth or WiFi, all of which those cameras support.
The three systems that are in fact smaller are the Nikon Z with f/4 zooms, the Leica M, and the Fuji X. The Nikon Z is smaller so long as you don't add any primes and stick to a 2-3 zoom kit (14-30, 24-70, and 70-300 AF-P on an FTZ), and the Fuji X is smaller but heavier. That said, the Fuji is also the best mirrorless system out there right now, if someone were buying new and had the money that would be the one I'd recommend, hands down, for most types of photography. And of course the Leica M has tiny lenses, but that's a whole different animal (and fully manual focus). In the next 2-ish years I also expect the EOS R and L mount systems to get the smaller part right.
A common misconception: they're not smaller, at least if we're talking like-for-like (this is a long topic about photographic equivalence, there are many articles on the subject), with a few exceptions. They are thinner since they don't have a bulky mirror box, but the Canon SL and Nikon D3k/D5k series are the same size, and their lenses are smaller, lighter, and higher quality, particularly the most recent Nikkor kit lenses. To get similar optical quality from a Sony E or Canon EF-M system, you need much bigger lenses, or an adapter (in which case you've just made your mirrorless camera DSLR-thick). The thinness does mean that smaller bags will fit them though, but until Nikon and Canon flesh out their line (and in Canon's case refresh the EF-M lineup) and force Sony to make decent kit lenses, you're either giving up substantial quality or getting a bigger system.I bring my mirrorless camera with a small zoom lens plus my phone. The mirrorless is significantly smaller than a DSLR. Some days I use mostly my phone, and other days it's mostly my camera. It partly depends on what type of photos I'm shooting. For motion, night photos, and anything where a zoom would come in handy my real camera does better. But some of that depends on how you'll use the camera. I don't get better results with my camera unless I'm shooting in manual.
The three systems that are in fact smaller are the Nikon Z with f/4 zooms, the Leica M, and the Fuji X. The Nikon Z is smaller so long as you don't add any primes and stick to a 2-3 zoom kit (14-30, 24-70, and 70-300 AF-P on an FTZ), and the Fuji X is smaller but heavier. That said, the Fuji is also the best mirrorless system out there right now, if someone were buying new and had the money that would be the one I'd recommend, hands down, for most types of photography. And of course the Leica M has tiny lenses, but that's a whole different animal (and fully manual focus). In the next 2-ish years I also expect the EOS R and L mount systems to get the smaller part right.