I recently stayed at Aulani for the first time (just me and my mom, no kids) and we also walked over to the Four Seasons, so I can give some thoughts but obviously my experience with the Four Seasons was very brief.
First off, I’ll say the two resorts are right next to each other, so it’s easy to walk between the two and eat at their respective restaurant, and hang out in the lobby areas.
Overall the Four Seasons seemed much calmer and less crowded than Aulani. Lots of nice seating areas to hang out and chill, with pretty ocean views. Their lobby is closer to the ocean, probably because their pool is smaller.
I think what sets Aulani apart is that it’s supposedly the only resort in Oahu built specifically around Hawaiian culture. It’s reflected in both the activities and the way the resort is designed (there are two tours you can take to learn about it) and there is a lot of live music throughout the day (maybe this is the case at the FS, I just wasn’t there long enough). This made me really love Aulani and feel like it was a really special place. As a DVC member, you’ll probably appreciate the theming!
The pool at Aulani is much larger and more extensive (lazy river, infinity whirlpool, grotto pools), but it’s also way more crowded and hectic. I didn’t mind the crowds, but my brief glance at the Four Seasons pool area it was much calmer (but also waaaay smaller and not as pretty… Aulani has a lot of vegetation planted around the pool).
I looked at the FS activity schedule while I was there (but not sure if it was complete since I wasn’t staying there), and it seemed like Aulani has more included activities (there are activities that cost extra too). I will caveat that you need to sign up at 8am each day for many of them, and I found you had to line up 30 mins early for the popular ones. So Disney

. They also have character meet and greets throughout the day.
Aulani’s spa was amazing and gets you access to a really nice outdoor area with different temperature whirlpools, lounge chairs, and water features. I could’ve stayed there all day! But you can do this even if you decide to stay at FS.
I also meant to eat at Mina’s Fish House at the FS, but ran out of time. I heard the happy hour is great there. So that’s also something you can do at FS even if you’re staying at Aulani.
I know you said you were going to stay cash, but I’ll just mention the value staying on points was great!