For many people hauling a camera with them in the age of the iPhone 4S is no longer necessary.
For many others the 8-megapixel camera in their phone, while a vast improvement over most other camera phones, just doesn’t make it from an image quality standpoint. Serious photographers want more camera to take along.
Taking your full size DSLR presents challenges of its own as that may mean leaving your camera in a hot car many times. Cars get crazy hot and before doing that you might consider investing a small amount of money in a min-max thermometer so you know exactly what temperatures your camera is being exposed to in the car or wherever else you’ll be stowing it.
Also consider that the temperature itself is not always the problem but the rapid change in temperature. Sometimes taking the camera from a hot car into an air conditioned space can cause condensation problems and reverse is true when going from a warm car to cold outdoor temperatures. A good camera bag can help with temperature transitions and so can a gallon-size ziplock bag. Seal your camera up inside and let the temperature equalize before exposing it to the air.
While still bigger than a camera phone, the new mirrorless cameras with larger four-thirds and APS-C sensors are certainly more conveniently portable than a full size DSLR, particularly when fitted with one of the pancake style lenses.
Sometimes having your camera means just toughing it out and packing it around wherever you go. Photographers on assignment do just that; not only carrying one camera everywhere, but sometimes two or three. They also eat, sleep and travel with them because hanging on to them is the best way to make sure their expensive cameras don’t get stolen.
How committed you are is up to you. Personally, I’d go with the smaller camera, but not when I’m on assignment. Then I carry the heavy stuff.