For my family (me, DW, DDs 11 and 12 years old) the extra day is hands down the better option. On our 2 previous trips we had park hoppers. We barely used them, and the few times we did we felt our day was disjointed and we got burned out. Our trips are usually 8 or 9 days, and we find its hard enough preventing burnout going to one park a day. DW is enormous, and too much travel always leads to burnout by day 5.
For our upcoming April 2018 trip we are going for 9 days and staying at Poly, spending 3 days at MK, and 2 days each at EP, MS and AK. We were originally going to go for 8 days and possibly use park hoppers, but decided to go the extra day and not hop. We are on DxDP. Each day we have a TS breakfast at either Poly or GF, pool time, get to the parks at about 1PM, and a late signature dinner. With our schedule, hopping would just give us a couple hours at each park.