I've only used neutron stars a few times to check it out, but yesterday I tried a white dwarf multiple times. It's actually not that difficult or dangerous. Whereas the NS will eat 1% of your FSD a WD seems a little more greedy taking 2% it seems. Apart from that I didn't see much difference except for the lower boost of the jump range. Maybe the WD scare is hyped a little bit? Like the fright of getting caught with illegal cargo making people boost into a station smashing it into a wall or a fellow CMDR to avoid getting a stupid fine?
It often depends on the size of the exclusion zone, some are little different from NS whilst others have barely any of their cones poking out of the exclusion zone. I think much of the ‘danger’ comes from explorer’s tales, when you’re 10’000lys from any station hull damage is far more of an issue. Certainly if it leaves you in danger of not being able to land on a planet to restock any materials you may need in order to get home.
All in all though the process is remarkably easy so long as you’re aware of what you’re doing, and not dozing off....waking up with a face full of Neutron Star (especially in VR) is.....interesting