This is my opinion
I have been a Lightroom user for 10+ yeras, I like it, but although it is better than it used to be with Fuji-X files, it still doesn't drag as much detail out of the images as some other RAW processors, but it does create pefectly acceptable (and pleasing images)
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@Jelster says it oversharpens Fuji files on Import, I have set up a preset that is used as an import preset (auto detecting a list of Fuji cameras I have entered) that significantly reduces sharpening on import.
More detail can be obtained using the Enhance feature.
Capture One does seem to extract slightly more detail but I can't get on with the user-interface, I've been locked into Lightroom for far too long. I have though been experimenting the DXO PureRAW, the latest version is used as a Plug-In with Lightroom making the use a lot easier. It is a very effective RAW processor, and excellent when treating higher ISO images. It too can oversharpen on occassions, and sometimes the greens get a bit carried away (easily corrected), but the level of detail it extracts is second to none. Having used it on my culled images (It can take quite a time to process), I then decide whether I'm going to process the DXO conversion or the Lightroom one, 90% of the time I head for the DXO one.
But all of this RAW processing depends on what type of images you want to produce, ultimate detail isn't the be and end all, especially with skin tones where a softer approach can be more pleasing.
Its all very subjective and down to an individuals preference. I would experiment yourself and find a workflow that suits you.