Heh... I loved Contra Rebirth (which is 2009 wiiware!) and never even wanted to try Neo...
Neo Contra got slammed upon release. In the end, I think reviewers were really, really unhappy with it not being a sidescroller like Shattered Soldier.
If you can cope with the Super C-esque camera angle, you'd realize Neo Contra encapsulates the spirit of Contra dialled up to 11. It moves past the bleakness and depression of SS and into cigar chomping, tongue-in-cheek territory.
Being shot out of a space station shaped like a gun.
Getting shot out of a volcano into a river.
Running on helicopter blades.
Old bosses like Kimkoh returning and given new life as a butterfly.
A Super C song given an incredible remix.
One of the greatest opening cinemas in gaming history.
The only complaint I have is that it does lack the intensity of previous games, but going for a no die run is still great fun and, like SS, a way to get the true ending and extra levels.
Looking back, as Bill and Jaguar do a Strider and ride away on a whale's back in the ending, it's clear to me this is where Contra ended, and everything that came after has just been fan games given official releases.
edit: I forgot Bill and Jaguar break the fourth wall and wave to you at the very end. What a game.