Capture One's LCC tool is indeed very good but any basic implementation makes a great job unless the sensor produces extra artifacts. The Dalsa 6um and smaller pixel sensors produce extra artifacts in the form of tiling and microlens ripple (Dalsa-based 40, 60, and 80 megapixel backs) which normal LCC won't correct, Capture One has good suppression for that (and my own Lumariver HDR if I too may do some sales work...
), which I don't think Phocus or Lightroom has, haven't really tested it recently though so I don't know for sure.
Fortunately the Sony sensor does not produce any (strong) tiling and no microlens ripple, so I think any basic LCC implementation will do just fine here, but I haven't tested Phocus personally.
There's one other factor too though, if the file has crosstalk in it the demosaicer may be put out of balance and you get mazing artifacts. Demosaicers that extract a very high amount of detail are generally more unstable and will not tolerate almost any crosstalk, the DCB mosaicer in some open source raw converters is particularly unstable in this case. The demosaicer in Capture One is a nice tradeoff between detail and stability so it can tolerate quite much crosstalk before it breaks down. I have not enough experience with Phocus to know how it behaves, but my guess is that it is too quite stable, becase I think that demosaicers designed for cameras without AA filters (ie all MF cameras) are more stable by nature.
Long post, but the message is that although I haven't personally tested Phocus with the Sony MF sensor and tech wides I think it's very likely that it will work out just as good/bad as C1, unlike for the Dalsa sensors where I think C1 is better.