I'm still using the C1 trial, but I've seen enough that I'll be using C1 as my main processor going forward. I think the answer to the "how much pain" question is going to depend heavily on how you currently use LR. With that in mind I'll describe how I use LR (v6), then note the areas in C1 that I've found the most awkward.
My goal with LR is to go from RAW to finished shot, preferably without doing additional processing in an external app. I cull my images in LR, make global and local adjustments in LR, and use LR for final image output. Unfortunately I often find that I have to dump the raw to a tiff and do some preliminary editing (skin touch up usually) in PS, before returning to LR; this is one thing I'd like to eliminate or at least reduce. I make only the most minimal use of LR's catalog system; I import into a default catalog, do my editing, use the "export folder as catalog" to produce a folder for archiving, then clear out the default catalog.
So now looking at C1 (and bare in mind I'm a C1 newb):
1) It took me a little while, but I found that I could sidestep their catalog system completely by using a default session and just browsing directly to my folder of fresh raw images. No more importing!
2) Blemish removal is different from LR, and it took me a while to adjust my thinking. On the one hand there's the spot heal tool. This is a fast, global tool that is aimed primarily at fixing sensor dust spots and acne (which it does very well) though it can and does work on other things. There's no control over the "source" of the area used as the replacement, and it's not a brush; you just target one circular area after another and C1 does a content-aware fill. You only get 100 of these spot-heals. A more flexible and powerful method is to add a clone/heal layer. This is kind of a hybrid of Photoshop cloning and the LR healing brush; you indicate a "source" area then brush over the area to be fixed. If the layer is designated as the "clone" type, well it's just like PS. If the layer is a "heal" type, then its action more closely resembles LR. However, note that you can only designate a single "source" area in each layer, so the amount you can fix in a layer is limited, and you only get 16 layers (whether heal/clone or adjustment) in total.
3) Local adjustments are also very different. In C1 you create an adjustment layer then draw a mask using a brush and/or PS-like gradient tool that indicates what areas will be affected and (to an extent) how heavily they will be changed. Then you go to the extensive local adjustment panels and dial-in your changes. Again, remember that you only get 16 layers in total.
4) Skin smoothing. After touching up blemishes, you can create a layer to adjust the skin tone explicitly, and make it more uniform (watch the C1 tutorial vid for this). Combine this with a negative clarity adjustment.
5) Undo / history. There is NO edit history panel. However, the step-by-step undo is deep, so you can roll back changes one at a time. You can also toggle any of your local adjustment layers on/off, and within each layer you can go to a specific panel and eliminate all changes made through that panel in that layer, or see what the image looks like with those changes temporarily removed.
6) Before/After. There is NO simple button to compare your current image with how it started out. However, you CAN create a virtual copy ("variant" in C1 terms) that matches the RAW in its unaltered state, and then view them side-by-side.
7) Panel/tool navigation. I find that navigating C1's panels and tools is a bit of a pain (no "solo" mode, and they self-close unpredictably to preserve screen space), so I am now actively learning all the keyboard shortcuts I can find. I never bothered doing this in LR, as I found the environment very intuitive.
That's about it. Obviously I'm taking longer over edits than I would in LR6, but that's because I'm still finding my feet. I do prefer the results I'm getting however - I believe it's going to be worth the effort.
One more thing: if you're using Win 10 be aware that there's an issue with C1 and the fall creators update: http://forum.phaseone.com/En/viewtopic.php?f=69&t=26863