Depends on the trip, but most of the time, I find the mugs to be worth it. This is especially true during the summer. I do typically grab some sort of breakfast thing at the resort food court before I head to the parks, so I will fill my mug before I sit down to eat, and then refill with Powerade in the summer before I leave for the parks. My park bag, most days, is a small backpack that has two water bottle nets on the sides. So I close the lid, and set the mug in the holder. Hands free. Then I have the Powerade to drink while I'm in line to get into the park. Also during the summer, I'm much more likely to take a midday break. I stop in the food court and fill the mug on the way back to the room. I may or may not take the mug with me to the park in the evening, but if I do, I'll usually fill on my way to the bus, and on my way back to my room at the end of the night. Depending on the timing of the midday break and afternoon thunderstorms, I may eat dinner at the resort food court before returning to the park.
This summer, it came in particularly handy. For some reason I didn't do as well with the heat as I typically do. I had a lunch reservation at the Polynesian, and happened to be feeling the effects of the heat when I got there. I arrived early because transportation took less time than I expected, so I stopped by Captain Cook's for Powerade while I was waiting for lunch time. Crisis averted, and another use of the mug. I also went over to the WL to take pictures before all of the rumored changes, and was able to use my mug there when I had lunch.
Figure a soda costs just about $3 and a bottle of Powerade is a bit more. The savings for me add up quickly. I generally don't put ice in my drink, so I find that the mug is plenty big enough for me. I also fly and RARELY rent a car, because I typically travel solo and find navigating Disney solo to be more than I want to deal with. I also feel safer getting on a bus than I do walking through a giant parking lot late at night. And by not renting a car, I save a LOT of money. So I don't do a grocery stop or anything like that.
I did not get a mug when I did a weekend trip, because then it would not have paid off. I also found the mug to not be worth it when I stayed at OKW. I was just too far from the refill stations. At the All Stars, it always pays off for me.