I prefer dice but I also have two dice rolling programs on my phone and, Back in the Day, I even used (someone else's) Dragonbone die roller.
All else being equal I like dice in and of themselves. They can be very decorative, they make fine gifts, and they are a physical reminder of the randomness of our largely mental hobby.
So: Dice first, then random numbers.
I have seldmom played diceless, but that's fine, too.