More complex, slightly heavier per power rating and more expensive than AC (by a long shot). Almost all have pesky (well not too pesky!) brushes - carbon pick-ups that pass an exciting voltage to the rotor windings - eventually they spark and require maintenance.
They are however easier (and cheaper) to control than AC. They are slightly more efficient than AC. For regen DC motors require complex regen controllers (expense again).
AC motors. Cheap and plentiful. Will not tolerate as much of a swing of voltage than DC, hence control of same is more complex. They give off more heat than DC (hence may need water cooling or fan-forced cooling independant of the main rotor). They are simpler than DC and as such they rarely need maintenance. In fact about their only maintenance is bearings or when the windings eventually short due to age or humidity - something that equally affects DC windings. AC is cheaper to repair/re-wind.
I think the power curves of AC and DC motors is similar but AC suffers from ‘cogging’ due to the control of this motor which is done by varying the frequency of the supply, unlike DC which is voltage controlled.
Overall AC is more expensive because of the cost of the controller. I’m not sure if this will narrow in time as both use similar electronics components, it’s just that AC control tends to be more capital intensive because there are more parts (and a slightly bulkier controller - I think).
My guess is AC is probably the future. A friend who died a few years back was a world-recognised expert in motor design and he told me 20 years ago he believed ultimately AC would win through.
Long live Edison’s alternating current motors!!