Pro: More space for the seats, wider seats less busy, a bit quieter, sometimes an at seat service (but not in DK and NO), usually less people.
Cons, a bit more pricey (also for seat reservations), but besides that no real cons. Not every train has a first class: like some local trains in Norway. You’re more expected to be quiet (not ideal for a family, but depends on your kids ofc :) ).
Seat reservations are included in Norway, not Denmark. Reserve seats via www.entur.no/en for Norway.
On your route, there are rather comfortable trains but the 1st class isn’t particularly special in Norway when it comes to seats. Just a bit more space, but nothing much extra. Some free coffee and tea as well, but not that special.
The Danish railways have excellent 1st class seats, but also very very comfy 2nd class seats on their domestic long distance fleet. The most comfortable 2nd class seats on any train in Europe imho.
Between Hamburg and Copenhagen they use older Deutsche Bahn trains now, which are quite nice but also comfortable 2nd class seats.
For this particular journey, I personally wouldn’t go for first class. There are better countries (UK, France, Italy, Central Europe,...)