While turbine housing size is hugely important, and plays a key part in how a turbo performs, on almost all turbochargers, compressor housing A/R isn't a performance issue at all, so don't worry about it, and stop quoting it, please.
The reason I'm writing this is because it's very common for people who aren't exactly turbo experts, especially when someone asks them what A/R the turbine housing is, or when they're listing one for sale, to quote the compressor housing A/R instead. The reason they do so is pretty understandable, as it's usually pretty noticeable on the front of the compressor housing, so it's much easier to spot than on the turbine, especially when still fitted to an engine.
While it's easy to spot, in 99% of applications it doesn't mean anything, and will be near as damnit optimal from the factory, and with no other options available anyhow.
For this reason, it's only really Garrett and BorgWarner who ever even print it on the housings- It's never mentioned on Holsets etc as they're all damn big and therefore pretty much perfect, and because of this there's no other options regardless.
Having said the above, and maybe it's a coincidence, but the only manufacturers where occasionally a larger compressor housing can benefit some turbos, especially when they're pushed hard, is Garrett and BorgWarner.
On Garretts the ones that benefit are things like the GT28RS, GT2871R, and even GT30R, that have optional smaller 'compact' compressor housings available, which make them direct replacement turbos on things like SR20DETs etc. These smaller compressor housings aren't the optimal ones for flow, but they serve a purpose to make larger than normal turbos fit in the stock space, so it's a compromise you may have to make in some applications.
On BorgWarners, some S200s, S300s, and S400s it's an option sometimes too. Thanks to the HUGE amount of OEM engines they're fitted to, Borgs often have a variety of compressor housing sizes fitted to what's essentially the same size turbo, and the bigger ones generally perform better than the smaller ones.
With Borgs it's become such a big thing that these bigger, higher flowing compressor housings have become known as "RACE COVERS", as they're proven to perform significantly better, despite the fact they're mostly the OEM parts from JOHN DEERE turbos; yes, tractors and so on! Of course, "RACE COVER" sounds sexier and sells more parts than "TRACTOR COVER", despite the fact most modern John Deere engines have some of the best turbos in the world fitted to them as standard.
Better compressor housings for Borgs have actually become big enough business that true aftermarket ones exist too, and they're not cheap, but they look cool...