Gotenks is formed when Goten is 7 and Trunks is 8, so the moves the character devises are decidedly child-like and are often more about the "show" of the move, rather than effectiveness. During his fight with Evil Buu, Gotenks does not transform into a Super Saiyan initially, in order to make the fight more dramatic. This ultimately costs him the fight.
Gotenks does however have the ability to go up to Super Saiyan 3, which is not seen in any other Halfbreed. It should be noted however that this does not mean that Halfbreeds were incapable of reaching the level, just that it was not shown in any of the series. Although they are two Halfbreeds combined, this does not make up one Saiyan and one Human, rather it still equates to an exact Halfbreed, with 50% Saiyan blood and 50% Human blood.
In one of the Dragon Ball Z movies, Junemba takes over The Other World, which causes the spirits of Hell to be unleashed on to Earth, as zombies. Gotenks makes an appearance, as Goten and Trunks are overwhelmed with the amount of Nazis that are revived, including a comical Hitler, tanks and all. Gotenks easily manages to hold off the evil army until The Other World has been saved by Gogeta.