You'd never think a game primarily focused on fanservice would be this, but the little cutscenes between Kasumi and Ayane in Dead or Alive Xtreme 2 actually work. Knowing how much of a crappy past both have had and their complicated relationship that's primarily consisted of Ayane spending the past several years hating her half-sister, seeing the two together not in the middle of yet another battle but instead just casually hanging out and enjoying each other's company is surprisingly sweet.
They finally put their differences aside in 5.
The final ending of the fourth game has Kasumi try to rush into the the exploding DOATEC building to try to save Helena. Ayane stops her.
Tina and Bass posing together for the audience and just having a nice father-daughter moment even though she just lost to him in 5's story mode.
Some of the specific opening, ending and combo attack animations between two fighters in Tag Team mode could count as this, especially if the fighters never actually know each other within the game's story.
It can be heartwarming for Virtua Fighter fans to see Jacky and Sarah fighting alongside each other when you consider all that they've been through and their pseudo-rivalry in their home series.