Out of curiosity, what issues are you seeing processing 1DX files in LightRoom (or what do you see better in DxO)?
I am only starting to use DxO and cannot use it for 1DX yet, but with Lightroom, I am not sure I would call them issues but I did notice that on some shots, there was significant differences between what I can do in LR4 versus DPP. In general I find LR4 to have more options, but here are some of the "issues" I experienced on some shots:
1- sometimes the sharpening is not as good in LR compared to DPP. My images are softer in LR with much less details compared to DPP and this is more significant on some shots but not all...This is even more pronounce if I use the DLO option in DPP (Digital Lens Optimiser) which LR does not have.
2- While I prefer the noise reduction in LR, sometimes it gives a feeling of "plasticity" to the image where I would not have that using DPP. Now this is a tricky one because in general I find the noise reduction in DPP not very good. But some shots I made in ISO 1600 for example dont look that detailed in LR4 but in DPP they look like an ISO 100 shot! Again this depends a lot on lighting, and how big is my subject in my framing (face most of the time).
3- the biggest things that bug me with LR and the 1DX are the colors are all off and so is the white balance. Everytime I import an image in LR from the 1DX the WB is off and the colors are not at all what they were in the camera. I need to play with everyimage to make it right. On the contrary when I use DPP at least the colors are all great and WB always good! I use LR for some Nikon files as well and I dont have this issue with Nikon files. Colors and WB are perfect when imported into LR. Even the exposure seem off sometime with the 1DX in LR but when I check in DPP everything is good. Hell at first I thought the metering on the 1DX was really bad, but I knew this was not possible, something else was happening here and must be how Adobe read the 1DX raw...
I have not figured out how to create of import the actual Canon picture style into Lightroom (I thought this was possible) but maybe this would help. Iin fact this is a cool features I noticed DxO has which I found useful...if it could read my 1DX files :-)
The key here is that I mentionned some shots, because the above observations are not consistent for everytype of shots.
This is why I am looking for an alternative then LR for the 1DX, something more flexible then DPP...