The faceplate you use screws to secure the piece you are going to turn. some people will glue a waste piece to what they are turning so they don't have to put screw holes in their work piece.
A chuck needs something to grip. So you either need to drill/turn one of two things. A tonguetenon for the chuck to clamp down on, or a (can't think of the term) holerecess to put the chuck in and expand it to hold.
Now the faceplate holds very well with the screws, so if you are doing heavy work by rounding out the bowl a face plate is very nice. A chuck is more likely to let the piece go if it is really rough or lopsided.
In both cases you can use the tail stock to help hold it secure.