to add:

most factory cars with upgraded springs/grippier tires do positively benefit from sway bar upgrades. in general, it reduces body roll which in turn keeps the tire contact patch more consistent with the pavement. (less changes in camber) it also speeds up transition time in a corner (the less the suspension has to travel, the faster it can do it) 

if you want to maintain the safety factory of the understeer bias that comes factory with most BMWs, make sure you upgrade to sway bars with the same front/rear ratio of stock. most aftermarket kits (from my experience in the 3series world) tend to go too big on the rear and you lose the factory balance (they aim for a more neutral handling characteristic) 

i cannot speak to the e39 chassis itself, and its inherent handling characteristics.

If you are trying to reduce tail-happiness you can make changes to your coilovers as well: http://speed.academy/how-to-fix-understeer-or-oversteer-suspension-handling-setup-tuning/