The character Jaguar is from the planet Edo. Edo is actually one of the previous names for the capital of Japan, Tokyo. He's also based on the samurai Yagyu Jubei Mitsuyoshi in both name and appearance.
Neo Contra runs on a similar engine to Contra: Shattered Soldier. They even feature similar menus, the order of levels played, and similar game-play style, although Neo Contra plays in an overhead view rather than the typical side-scrolling view the Contra series plays as.
In Mission 5, an alien bug is shown in the background on a bridge. That alien can't be destroyed.
The ending theme in Neo Contra was reused as "Rock It Breaks" in the Konami wrestling video game "Rumble Roses XX".
The helicopter the characters ride on in Mission 4 is Mr. Heli-Robo, the helicopter that attacks the players in Stage 1 of Contra: Shattered Soldier and later gets crushed by the stage boss as well as the mini-boss in Stage 6 prior to the final boss battle.