Would a starship that was propelled by magnetic monopoles fly faster and longer than ion engines (assuming magnetic monopoles exist) of course.
Which is to say, neither yes nor no. The question as asked simply doesn't have an answer. It is ill-posed, because it is trying to compare things in two different categories.
Magnetic monopoles don't really do anything interesting in the way of propulsion directly. What they're good for is power production--you might be able to use them to catalyze baryon decay (i.e., mass-energy conversion), or to catalyze fusion. That's very useful for space travel, but you still need to design the rest of the rocket!
"Ion engine", on the other hand, specifies a particular method of accelerating a particular class of reaction mass to produce thrust, but says nothing about where the power comes from. You can have chemical powered ion engines, solar powered ion engines, nuclear fission powered ion engines... and if we had monopole reactors, you could have monopole-catalysis-powered ion engines.
In which case, a ship propelled by magnetic monopoles could very well be exactly the same ship as a ship propelled by ion engines, and it would fly exactly as fast and exactly as long as itself. And you could easily build monopole-powered rockets that don't use ion engines that are faster and have better endurance than non-monopole-powered rocket ships that do use ion engines, and vice-versa, depending on what other engine technologies are available and what the intended mission profile of each type of ship is.