It's probably worth distinguishing Moving Iron (MI) vs. Moving Magnet (MM) as well. MI usually has the same output and capacitive considerations as MM, but its design allows for less weight at the other end of the cantilever. Also, since there are some advantages (inductance?) to low output owing to fewer coil winds, Grado, that great purveyor of MI carts, makes some low output (0.5mV) versions of their premium wood-bodied cartridges.
Also, there are some other things that can be done to improve the responsiveness of MM. The use of neodymium magnets could dramatically reduce the moving mass. The Audio Technica AT150MLX uses two tiny magnets in a V configuration for improved stereo separation and 6-nines copper throughout. I'm not sure if it uses neodymium magnets, but it's very transparent, lively, and quick, especially for an MM, and especially for a cart that can be had for $250 shipped.
There are plenty of good cartridges from CartridgeMan and SoundSmith, and some respectable ones from ClearAudio, Rega, and others that keep MM designs competitive at least up to the $1.5K range. Their higher output can make for a lower overall S/N ratio when the entire signal chain is taken into account. There's less noise at the speaker end from a 5mV source than a 0.5mV source.