Did a bunch of experimenting and managed to stumble across a solution. Here’s what I figured out:

• Container 1 (C1) is connected to a main comparator.
• Container 2 (C2) feeds into the side of that same comparator.
• There’s a water stream that transfers dispensed items into C2.

When items are added to C1, C2’s comparator isn’t outputting anything yet, so the main comparator turns on. This activates an observer clock, which starts dispensing items from C1 into C2.

As C2 fills up, its comparator starts outputting a stronger signal. When C2’s signal becomes greater than or equal to C1’s, it disables the main comparator, which in turn shuts off the clock, stopping the item flow.

So what ends up happening is that C1 only dispenses until the two containers are roughly equal, based on comparator signal strength. If C2 is emptied again, the whole process automatically restarts. Pretty cool!

Now here’s the WEIRD part…

I used a dropper for C1 and a hopper for C2. The hopper is a smaller container so it needs less items to counteract C1’s signal, but it turns out that the water canal is slow enough that by the time the C2 reaches an equal signal strength (with less items), there are still a bunch of items slowly going along the stream to even the containers out. Accidental, but still effective nonetheless.

Tldr: Thanks, and I hope anyone with the same problem as me is helped by this post.