Madrid public transit is pretty comprehensive, but not particularly cheap or accessible. The rail is a bit archaic to use (single use tickets require source and destination stations despite being mostly one fare zone), station layout is fairly confusing at the bigger stations IMO. Perhaps most importantly, the stations are often pretty deep requiring a lot of waking -- not a problem if you're able bodied though.

I didn't use the bus system at all so I can't comment there. Barcelona in comparison has fairly easy to navigate stations and a much friendlier fare system.