Well, to each their own on a person's likes and dislikes. For me, I enjoy watching animes that have Giant Robots. I know there are series that tend to do things over the top when is comes to the mechs power(Gundam, Gaogaigar, Godannar), but that what makes it enjoyable to watch. But I also enjoy watching animes in which the giant robots are not overpower.
Full Metal Panic is one series that comes to mind. The majority of the mechs (Armslaves, Savages) in that show do not power up to an insane proportion in which they take out an army of mechs with one laser beam or have extreme super speed. When you see these mechs in action, they are used in a tactical sense in which the surrounding are utilized to gain an advantage. Even the mechs that are equipped with special technology such as the Larabda Driver (ARX-7 and mechs from Amalgam), that technology has been seen used to block physical attacks such as bullets and missiles, hold up a very huge mech, and return energy back at an assailant. I also enjoy the story is done and how the characters are presented.
Another anime that I enjoy watching that does not have overpower mechs is Betterman. Even though the NeuronoiRAB required pilots with special abilities (and two of them had very powerful psychic abilities), the mechs themselves were not overpowered with weapons. The abilities seen were mostly analysis and using a specific attack either countered or nullified an enemy. Plus, the mechs in this series where mostly being thrashed rather than it being the other way around when they were involved in their perspective fights, though I did enjoy how the mechs utilized on their analysis and counter abilities to win some of their battles.