Business class vs premium economy

There is a great deal of variance depending not just on the airline, but the specific route flown, and it pays to do your homework with sites like SeatGuru. The rule of thumb these days, though, is:

• Premium economy gets you more legroom (often 36-38" (91–97 cm) instead of the usual 30-32" (76–81 cm)), wider seats, a tiny bit more recline, and, on some airlines better food
• Business class gets you a lie-flat or angled bed and much better service all around

But there are exceptions in both directions, and the best premium economy seats & service (eg. some Air New Zealand 777s) are better than old-style non-lie-flat business class seats (eg. Hawaiian's older planes).

I have flown Premium Economy with Singapore and especially Lufthansa a lot. The existing answers cover most of the ground already.

You have more space, not only for legs, but very importantly for your elbows as you don't have to share the arm rests with your neighbor. Also service and amenities (toothbrush...) are better.

I prefer Premium Economy a lot over Economy. Of course, business is nicer, but I wouldn't pay the usual additional fees for private flights. You may consider this though as it is your grandpa visiting.