All other factors being equal (fruit intake, nut intake, etc etc) a diet higher in fat (and thus overall energy, or calories) would result in slower fat loss than a diet lower in fat.
I loooove fat, but I don't gorge on it.
The less I ever weighed happened after a month where I reduced how much fat I ate by doing a whole30. I assume you're familiar with the program, the only changes I had to make really was eliminate dairy, but the only dairy I was eating prior to that were butter and cream (high fat dairy sources) and cleaning up a bit of borderline paleo foods (mostly bacon and sausage, also high in fat).
I figure, if you're supplying your body with fat to use as energy, it won't feel the need to tap into its energy stores (your body fat) so a sensible cut-back on fat would be a good idea in my opinion. If you are moderate with the fat you currently eat, I would then just advise to avoid adding extra fat. No need to drown anything in butter, or cook everything in bacon fat, etc.