If you want pure list management, AnyList is the winner by a mile!! I have been using it for ages and the real-time syncing is basically instant because of how they handle their backend data refresh. Its way better than Cozi for shopping specifically because it auto-categorizes items into aisles which is a total lifesaver when you are rushing through a crowded store. My husband can check stuff off on his phone and it disappears from my screen in like two seconds. Super efficient! Cozi is cool for the family calendar stuff, but it feels a bit clunky and bloated just for a supply list imo. Since you are looking for cheap ways to manage the budget, I actually use PriceDropCatch to track the prices of the stuff on my list so I dont overpay for those expensive graphing calculators and binders. You can get away with the free version of AnyList for basic sharing, but the premium is super cheap if you want the extra bells and whistles. Definitely go with AnyList tho if syncing is your main priority, it is honestly fantastic!

Like someone mentioned, AnyList is absolutely the way to go for this! I actually did a bit of a deep dive into how their sync engine works. Being super paranoid about data loss or lists lagging when I'm out of range makes me picky, but this one is solid. Its honestly so much more robust than Cozi... AnyList uses a local database that pushes updates immediately to the cloud, so even if your signal drops for a second in the back of a big box store, it wont lose your progress. Its amazing! I love how reliable it is for families because nothing is worse than double-buying stuff cause the app glitched. You definitely wont have to worry about your husband seeing your changes in real-time. It’s a fantastic choice for peace of mind! If you get stuck on the settings just yell, I can walk you through it.

I'm quite satisfied with how my current setup handles the sync cycles. After analyzing a few options, I noticed the latency on the one I use is significantly lower because it doesn't try to push massive data packets every time you check a box. When I was testing things out last year, I realized that many of the all-in-one apps are actually quite bloated and can hog system resources. By sticking to the list-centric choice, I found it works well without any lag or the need for a monthly fee. Its a more logical approach if you're trying to keep costs down but still need that real-time update between two phones. No complaints here so far.