I find the wording and usability a bit confusing, "Older Dest", "Newer Dest", etc. I think that dialog needs to be overhauled entirely for this approach to work, cf. to how windows uses command links for that (they're also quite hard to grasp at a glance imho), not sure, perhaps usability knows a good solution for this problem.

The "Apply to All" button is used for all choices, including "Overwrite", "Skip", and "Rename".

NVM, I should have looked at the pictures, not only at the "Removed checkbox" description...

I propose that "Apply to" be taken out of the checkbox/combobox, hence Apply to: "combobox"

And I propose the labels:
"This File Only"
"Every File" (or Every File in Transit)
"Destination, if Older than Source"
"Destination, if More Recent than Source"

Otherwise, nice patch! +1

P.S. I know they're "wordy" but the options are actually very complex :D I think we can risk it. The problem is that if it says "Older Dest" it sounds like a destination that's older than some other destination and not the file being copied.

You could use "Destination, if Older than Source" and "Destination, if More Recent than Source"
OR use the source as a reference point, hence
"Destination if Source is More Recent" and "Destination if Source is Older", respectively.