Is it easy to convert a cylindrical to mortise lock, or should I just install a deadbolt?
Fitting a mortise-lock is fairly straightforward and only requires basic woodworking skills, really. The two most important tools you'd need are a drill bit of right size for the lock and a sharp chisel of the same width (an additional wide chisel for the sides is useful, but not essential).
Regarding the faceplate width, you'll have to check the size of your existing holes against the size of the plates on the handles you want to use, allowing for the difference in centre position between the cylinder lock and the handle of the new mortise-lock.
Assuming that you can find handles/faceplates to fulfill this requirement, then it's down to your skill, but be aware that drilling the rebate for the mortise will be made harder because when you hit the existing hole, your bit will want to move. I'd suggest drilling the holes which meet the cylinder hole edges first, and using an auger/straight style bit (as opposed to a flat bit). That way you have the start of the hole to help keep the bit from wandering.
Obviously the dead-bolt option would be far, far, simpler. Only you can decide which to do.
One thing which is worth considering, however, is the security-level of these locks.  Sure, you can get cheap-ass mortise locks, but they're cheap precisely because they are rubbish, probably only 2 or 3 lever, and dead easy to pick. A cylinder dead-bolt will be orders of magnitude more secure, but probably easier to kick-in.
Finally, are you even able to fit a mortise-lock in that position? 'Panelled' doors which have a cross-member morticed into the side-rail should not have mortice lock within 3&quot; or so to avoid weakening the door.