I mean, a quick glance at the dungeon journal would show you that in this expansion, Normal is the mode where they removed the mechanics from Heroic, and LFR and Normal have the same mechanics. They might be easier on LFR to handle, but it didn't seem that way when I did it.
I did normal, and I did LFR. LFR was "harder". They were both easy enough that I could've watched a movie while playing. LFR isn't inherently harder, but the normal groups on group finder require 845+ ilvl on the low end, with many asking for 850+, while LFR is 825+ to queue. Every boss I did on both Normal and LFR, the Normal boss died quicker, less people died, and we wiped less. All the mechanics were basically the same, and ignored in similar ways.
LFR is tuned lower than Normal, but unless people stop being so picky with their ilvl requirements, Normal becomes "easier" because you are required to almost outgear the content to get invited and the players applying are often better because the worst players are too gun shy to apply to normal groups.
So yes, the same ability does more damage on Normal, but it is very possible that on LFR (which has all the same mechanics as normal) every ability will be more deadly, every boss will die slower, and there will be more wipes than on normal. I think that qualifies as some type of "harder", unless all you mean by harder is "boss has more HP, abilities do more damage"