IMO, the organized tour/activity is worth it solely for the logistics. I didn't do it through Aulani as we did it through Discover Hawaii Tours when we were staying in Waikiki, but the benefits of the tour are the same and I presume they operate similarly. In my experience, they facilitate the tickets for you that coordinate with your tour timeframe. You are free to tour the free portions yourself - we had about 2 hours to do this before our tour time. We were not rushed to get back to the bus after our Arizona Tour. I think they picked us up from our Waikiki hotel around 6:45, we got there around 7:15, our tour was 9:15, and we were back on the bus by 11.
Doing it on your own can give you more flexibility, but can also put you in a pickle from a timing perspective. Currently, tour times can only be obtained online a week in advance and its very limited. If you're not lucky enough to obtain one, you'll have to arrive quite early to wait in the standby line to obtain a tour time. The further back in the line you are, the later your tour time will be. If you're there at 8am and get a 2pm tour time, then you'll need to occupy your time between 8-2 somehow. You can fill a couple hours touring the free portions, but not that full time and food options are limited. It also doesn't allow you time to do the Missouri or anything else offered there. Leaving and returning can be tricky because there can be parking challenges later in the afternoon, and its also not advisable to leave bags or anything like that in your car because theft can be rampant at Pearl Harbor. So, it makes it difficult to plan your day and you'd have to dedicate a full day to it, just in case.