Mega Man vs Metroid
Connection:
Both are blue-themed fighters with very high tech armor and powers
Both possess arm cannons (X Buster and Arm Cannon respectively)
Both work with a law enforcement organization (The Maverick Hunters to X and the Galactic Federation to Samus)
Both have purple-themed rivals who are responsible for what they've become (Vile to Mega Man X and Ridley)
Both also have upgraded armors (Ultimate Armor and Varia Suit respectively)
Both also have made crossovers from other franchises (Marvel vs Capcom and Super Smash Bros respectively)