I used C1 years ago and changed to LR mainly for the integration with Photoshop and the asset management features. I recently changed over from Canon to Sony and this has given me the impetus to look at other raw converters again.
I must say that comparing one converter to another is very confusing - and I would very much welcome your own experience with these converters. Also, I am only comparing the raw conversion features here, not other features like slideshow, maps, books etc as Lightroom is clearly way ahead there.
The first thing I would say is that both have strengths and weaknesses but that these can be quite easily equalized in Photoshop (or with plug-ins). This is fine for me as I always finish off my images in Photoshop, but I've found that there is nevertheless an advantage in using one converter over the other for specific types of images.
So first of all resolution. I can see absolutely nothing between the two (at least not on Canon 1DsIII and Sony A7RII images).
Sharpening: There's nothing between them IMO. Both use an Unsharp Mask type sharpening (in spite of the claims that LR uses deconvolution when the Details slider is swung one way rather than the other) and they are both OK if that is the only option. However there's no doubt that deconvolution sharpening in Focus Magic or Topaz is significantly better for capture sharpening.
Noise Reduction: again, nothing between them IMO. Fine for color noise reduction, but I wouldn't use either for serious luminance noise reduction.
Tonal adjustments: On the whole apples for apples here. However if an HDR-look is wanted then the C1 HDR sliders are very good. On the other hand, LR's Shadow and Highlights sliders gives a more natural (less HDR-ish) look, which in general I prefer. Having said that, these effects can be achieved using the Levels or Curves tabs, so having the HDR sliders is very nice.
Clarity: Nothing much between them. However C1 has the Structure slider which is clarity at the micro level and it is very good at bringing out small detail (and also noise).
Color Balance: C1 is better here as it gives control over shadows, mid tones and highlights, while LR only gives overall control plus shadow control (in the Camera Calibration tab). C1 also gives full control whereas LR only gives tint control (plus Red/Green/Blue primary adjustments which are only really useful to correct camera calibration, not to adjust the image hues).
Color Editor: Again C1 has a definite edge as it is makes it much easier to target color ranges (whereas LR only allows changes to specific hues, like yellow and aqua). The Advanced tab of the C1 Color Editor is particularly powerful.
Local Adjustments: C1 has a major advantage over LR here as far more local adjustments are possible and the use of layers is really good.
Lens Correction: LR is better IMO, partly because it has support for far more lenses and very quickly after they are released, and also because the distortion corrections are more powerful.
Effects: LR has quite a big plus here with the Dehaze slider which can rescue images that would otherwise be trashed.
Camera calibration: In principle I like C1's use of ICC profiles but in practice I think LR's use of DCP profiles which can be quickly and easily modified for different lighting conditions is better.
So these would be my impressions on a detailed level, not taking into account entirely missing modules in C1, and C1's poor integration with Photoshop (no smart objects for one major thing). But if I had to make a choice between the two, purely for raw conversion and assuming as much as possible to be done in the raw converter, then I would pick C1 because of the color editor and local adjustments.
Having said that, what I've found is that the two converters handle different images quite differently. This is something that has made it very difficult for me to decide which one to opt for. I've found, again and again, that I prefer the way that one converter renders a particular image and I've found it difficult to achieve the same look with the other converter. For example, I find that photos of buildings where there is a big dynamic range tend to come out much better in C1; on the other hand, pale seascapes look more natural to me in LR. Also, creative effects are sometimes much more easily achieved in one converter than in the other (in spite of C1's more advanced color editor) and this seems to be quite image-specific.
If the integration between the two programs had been better (and better integration between C1 and PS), I wouldn't have hesitated to use the two, depending on the image. But unfortunately the integration is really very poor and I particularly dislike the way that C1 does not keep the sidecar files with the image and doesn't put the adjustments into the DNG files.
So I'll cough up the $50 for the Capture One Pro (for Sony), but I wouldn't pay the full price for Capture One Pro, even though I have a huge number of Canon files that I still need to process. If Phase One improves the integration with Adobe apps then I will buy the full version because it has some really nice features and does a better job on some images than does Lightroom (and vice-versa).
It would be really good if raw converters became a bit like plug-ins ... in the sense that one could use one converter for a particular type of image for which it was particularly strong, and another converter for another image for which that converter was particularly strong (perhaps using DxO for images needing serious lens corrections, for example, when the normal everyday editor was C1, say).
I would certainly very much welcome a different perspective as I'm still somewhat conflicted, to be honest
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Robert