Originally posted by biz-engineer Or are they equivalent?
Depends on what you mean by processing
Speed of importing a folder full of images and rendering standard previews? All three are OK. Speed of sorting and culling 1000 freshly imported event photos? Lightroom by a mile. Dynamic processing of working changes (eg as you move the sliders around while working on an image)? C1, DxO, LR. Speed of processing an image into an export format (eg saving to TIFF or JPEG)? C1, DxO, LR.
Each can have a different working 'speed'. Sometimes that has nothing to do with the programming speed. I find Lightroom, for example, the fastest program for sorting, rating, culling, and then processing big jobs where I may need to process 1000 event DNG's in one sitting, simply because LR is designed to support that kind of workflow.
But generally I would rate their program speed as:
1. C1
2. DxO
3. LR
But, once again, it depends: on what processing you have done (NR, lots of spot adjustments etc), whether the image is a big file-size high-ISO shot, and so on.
DxO and I think C1 also can offload some processing to your GPU (CUDA if you have an NVidia card), which does potentially speed things up. Lightroom (as yet) ignores the GPU, but v6 of LR will apparently support using GPU horsepower better.
tl;dr - you need to try them out on your computer. How you work will also shape your perception of speed.