I'd be interested in a clarification on several of these points, which by way of being on your list implies they are better than LR or do not exist in LR.
I can't speak to all of Paul's points, but here are my thoughts:
1. Adjustment layers that operate independently of each other up to 15 per image: Is there a functional advantage to adjustment layers over the LR paradigm of unlimited adjustment brushes and gradients?It's just easier to go back and find a specific adjustment brush or gradient. I've gone back to images months later to make changes. In LR you have to guess and figure out what gray dot to pick and edit. Also I may forget I had a brush for some specific change. I go in, add a brush, then later find out I have two "sky" brushes. Now I have to change them both and keep them similar. C1 you can name the layers to remind yourself. Fewer clicks as a result too.
4. With version 10 new sharpening options which use deconvolution: I believe LR also uses deconvolution when you move the detail slider past 50. Is the C1 sharpening superior?The nice thing about C1's implementation is you can apply deconvolution only. It is applied separately from sharpening.
4. With Version 10 sharpening options for output (depending on web view, printing etc): Is the C1 implementation more sophisticated than the LR low, medium and high options? I'm not sure it is more sophisticated but it is more adjustable. They give you sliders with default settings instead of default settings with no options. Whether this is good or bad depends on how much you like LR's fixed options. For example, I'm fine with LR's default std for glossy paper, but for matte paper I would like something in between std and high. I haven't done any tests yet so I don't have a sense for C1's sharpening as it appears on papers, so I still use LR to print from. For now...
7. Ability to control WB per layer (huge for my workflow): Is this functionally different from creating different WB in adjustment brush or gradients in LR? It's just easier (for me at least) to use sliders with real color temp vs. the color picker approach of LR. You have sliders in LR too but the implementation feels different. Frankly this might just relate to the other layer-approach benefits above.
8. ease of copying adjustments from one image to another: There are multiple ways to do this in LR. How is the C1 implementation better? Just fewer clicks. In C1 shift click and you are done. This does depend on how you approach this type of editing. It really shines when you are experimenting with settings in a specific adjustment panel/tool.
9. Side by side viewing (I have never liked LR's way of enabling this, just too complicated for me): Does this comment include LR's reference view? If so, how is the C1 implementation better? I'm not sure of Paul's original comment, but I suspect it did not consider LR's new-ish reference view. Sometimes I like LR better for this, sometimes not.
Dave