There are several elements that don't change based on the characters fighting that can get a little weird sometimes.
Chiaotzu's ultimate attack, "Goodbye Mr. Tien", has Tien randomly screaming Chiaotzu's name in the background during the explosion. Partially because of this, the attack name takes on a whole different meaning when Tien's your opponent...
Every character in Dragon Sim mode in 3 has the same possible events that are randomly drawn from. Yes, Chi-Chi is ordering the likes of Frieza, Broly, and Omega Shenron to sit down and do their homework.
The Saibamen's ultimate attack leaves the opponent in Yamcha's classic, trademark pose regardless of who it is. It's quite an unusual sight to see the likes of Broly, Omega Shenron, and SSJ4 Gogeta crumpled up and helpless on the ground.
In Budokai Tenkaichi 2's Fusion Reborn Story mode, after Gohan defeats Bojack and Zangya, both Frieza and Cell comments how terrible Gohan's Great Saiyaman outfit is.