Have used Emirates economy 10+ times over the last month to and from DXB from BHX, LGW, MAN, LHR and throughout the ME, on both A380's and 777's, all times travelling with both a laptop backpack and also my holdall, which goes against the rules in terms of number of items but both conservatively sized and not excessive.
Not once was I stopped, checked or asked to check anything in but then I did go straight to departures for each flight and I don't recall seeing any scales/sizers (although I'm sure they're there).
Some of the bags I saw being put in the bins were ridiculous. I would just say use some discretion and don't bring anything too large and you should be fine. Worst case scenario it gets put in the hold free of charge and add's 20-30 mins in baggage claim.