I think your pops might have been joshin you a bit, the 30-06 isn't underpowered, it's just obsolete. As a versatile all-around cartridge for people shooting cast loads, or they got a rifle given to them in this caliber it's fine. You can find ammo for it anywhere, and there's lots of loads available. The issue with 30-06, and why it was replaced, is because it's obsolete. New powders and modern steel chambers have kept it on life support, along with modern bullet construction.
The main issue I have with 30-06 is that it has the trajectory of a basketball.
It's also a long action cartridge, the bolts usually wobble and require extra effort to cycle. This also makes the rifle longer and heavier, and can reduce accuracy if scoped.
You'll rarely see a 'tactical' style rifle chambered in this, if that's your thing.
With the 308win cartridge, there is no reason to own a rifle in 30-06. Insert comments like "Well I been using it for X years blah blah" below