Obviously 1st class is "plusher". Probably the main difference is that the width of the coach in 1st class houses 3 seats instead of 4 seats in 2nd class.
The result is more spacious seats and aisles. It also means you have "single" (no one beside you) seats on one side of the coach and "double" seats on the other. On the "single" side you can also have two seats opposite each other. This means 2 people can be "isolated" and facing each other.
Most 1st class TGVs are equipped with plugs for computers. In 1st class you can also reserve a taxi which will await you on arrival at your destination. This service is only available during weekdays and on some destinations (mainly arrivals in Paris and other major stations). This service is free of charge, you just pay the normal taxi fare.
In 1st class, on the left you see the "single" seat.
On the right the double seats.
A "single" seat in 1st class.
2nd class "family seats" for 4 people
1st class "family seats" for 4 people