Driven a couple of Classics, but never owned one, own a P38 and have owned (and repaired) a Disco 200TDi (a Classic in drag...okay sack-cloth!!).
Ignoring diesel -v- petrol differences, in my opinion the Classic isn't a patch on the P38 to drive, neither are hugely difficult to keep on the road, neither cost a fortune if you can wield a spanner (and use a forum like this one) but the P38 has 4 crucial advantages...
1. No rust to speak of.
2. Space proportionate to the amount of road it hogs (rear seats in a Classic/Disco 1 are a bit of a joke for anyone over 6 foot, a P38 is almost limo-like in comparison).
3. A boot that can actually take a proper load without removing the spare wheel...or worrying the load will disappear through the rust hole in the floor
4. Much nicer/roomier interior (quality of plastics/switchgear aside...frankly both are rubbish!!).
Both (for their respective time) genuinely provided an amazing compromise between on-road and off-road performance; both take you from A-B in true comfort regardless of prevailing conditions and both contribute significantly to the annual bonuses of oil industry executives. However a P38 has 25 years of chassis/suspension development to its advantage.
Day-to-day P38 for me without question, but I wouldn't turn my nose up at any Classic (but I would invest in welding classes!!)