We installed a quaife core on mine, and after a few thousand miles the diff bearings were done due to faulty installation. Got a scrap yard diff and had the actual quaife importer do the install with the same old core. So far no problems. Point being, don't cheap out on installation if you go for an ATB core.
However one wheel peel is not really a thing on the Z4 except in the rain. Seems most people get LSDs just because it is cool. Im sure you know what you are getting, but I just want to mention it to others reading.
I do not recommend getting an ATB LSD for the Z4 unless you
1a) want to practice drifting in the rain and/or
1b) care about lap times on a track, looking for a more planted rear end when exiting onto curbs etc.
2) Drive with DSC=off. In good conditions, there are really no benefits to be had if you drive in normal mode imho. Traction control will have already decided to kick in, when the diff starts to react, no matter open or LSD. That is my experience.
Know that the OEM diff is absolutely usable for drifting in the dry. If you want more grip on the street try better tires first. If that doesn't work, try even better tires. A diff wont really increase straight line grip in normal conditions.