I loved Renegade and the original Double Dragion, and was really pleased with the sequel. Although it's been dismissed by some as merely a remake, Double Dragon II was a step upwards from the first game, and was a lot tougher to beat.
Firstly are the new control method and couple of new moves that have been added- the all-conquering back-elbow is now a more balanced move, and there are new flying kicks. Weapons also are different, with shovels, chains and haystacks replacing some of the older ones.
Although some of the scenery is very similar to the first game, the range of enemies is now a lot wider, especially the hulking end-of-level bosses. It's about the right length for an arcade game, with a good difficulty curve. Graphics and sound are close to the original (the same level of detail, but slightly more color). There isn't much of a story, but there is a good twist at the end.
Overall, I'd say this was the best DD game- I thought the series went downhill with the sequel (where you had to insert real money in order to buy things from the shop!), and the one-on-one versions that followed.