That's very general, so my answers will be too. No one system works best everywhere though.
Quicker to install. (Pylons and beams can be cast off site and trucked in to be installed at night or in low traffic times.
Less disruption to traffic during construction. Less disruption to businesses along the route.
Once finished, a straddle-beam monorail (like Seattle, Disney, or Las Vegas) takes up roughly a half of a traffic lane. Light rail runs in the road and takes at least a whole lane, creates confusion at crossings, and absolutely destroys cars when someone makes a mistake. In fact "light" refers to its capacity. The trains are actually built heavier to withstand the inevitable collisions with vehicles.
Rubber tires on concrete are quieter than steel on steel conventional rail.
Trains can be automated, like in Vegas, whereas light rail, heavy rail, and anything else running at street level must be driven by a human.
Monorails never hit cars. (Having said that, I bet I will later think of an example where one did.)
There have been less than 20 passenger deaths on monorails since their first use in 1824. (1821 if you believe the Russians.)
The public generally believes monorail is more attractive running through neighborhoods and retail space.
Rubber tires can climb 10% grades. Steel on steel can climb 3% grades.
I'm sure there's more, but I'm with friends and we're heading to a Yächtley Crew concert.
Edited to add a photo of me driving the Seattle Monorail wearing my WDW uniform.