.32 acp/7.65 browning is a semi-rimmed cartridge, which can potentionally cause feeding issues across all weapon systems. .380 is rimless.
.32 acp can use factory metal mags and has the factory look. I think all the .380 acp mags are not only straight but also polymer, so may be less robust than original military metal...
.32 acp is more expensive for factory ammo, but reloading costs are about the same between the two calibers. Probably also depends on if you're already stocking one or the other caliber.
And while I care and am partial to .32 acp for its increased compactness vs. .380 acp for pocket carry, it matters less here...
Ballistically, I'd *think* the .32 acp probably performs better at distance for offensive military/(combloc)police use, and I'd also be partial to it ballistically/recoil in a f/a scenario. Semi-auto and today, barring WROL, you're probably ahead w/ .380 for any serious use scenario.
So I think it really comes down to whether you're a collector or shooter -- do you want as authentic as possible with all the OEM accessories, pouches, tooling/repair kits/gauges, etc., to work, or do you want a more modern and perhaps more practical take on the original?