I bought several new Milwaukee FUEL M12 ratchets and nut driver. The ratchet are bare tools and the nut driver was in a kit with two 2.0AH batteries, charger and case. I see there is a 3.0AH Compact and 3.0AH XC with a larger square base. If both batteries are rated at 3AH, I'm under the impression that run time is the same on both and that the only difference is one is more compact. I know there are 4.0 and 6.0 M12 batteries that give you more run time but see there are two versions of the 3.0AH. If AH is run time, then both should have the same run time. Not an electronics expert and couldn't find any info as all comparisons online are 3.0 vs. 6.0 and not seeing anything comparing both the 3.0AH batteries.
In theory, runtime should be the same for light usage.
In demanding applications, the XC battery will have a slight advantage. XC batteries also give certain tools (mainly drills and drivers) a slight bump-up in power, but that only be the M18 lineup - I don't think I've heard of similar for M12 tools.
Because an XC battery pack has twice the number of cells (6), the current draw from each is lower than if you only had 3 cells. For light duty tasks, there's no difference. In heavier work, the compact battery will increase in power output, and also internal temperature. The XC battery pack will increase in power output, but that output is shared by two series of cells, resulting in lower operating temperatures.
Cooler battery packs tend to run longer than hotter ones, and you also have less risk of overheating protections kicking in.
If you don't care about battery size or weight, look at potential pricing differences.
The compact battery is smaller, the XC battery might be convenient, as it allows for certain tools to stand up on a table or floor, at least easier and more stable than a compact pack.
On top of all that, from what I've seen, on-paper specs for 3.0Ah cells are lower than for 2.0Ah and 2.5Ah cells. I'd go with one of those lower capacity compact battery packs, or an XC pack if I needed more runtime.