you can use both.
Rigging is the way to go for legs, arms and other extremities, (mostly), so you'd want to rig him as you would a normal 'humany type character', coz he'll mostly be standing upright, rather than on all fours.
If you can model him in a stand-up kind of position, then he'd be pretty straight forward to rig, and you could use morphs on the one whole object. (piglet).
You might want to bone his ears as well.
(i see he has no fingers, thats cool. none to rig)
Using seperate objects for 1 character has points for and against.
If you do use seperate objects on piglet, then you won't have any skinning issues, and you can be a lot 'free-er' in your animations, without having to worry about deforming meshes.
But the downside is, that they will look like seperate objects because theres no proper joins like there would be in a single mesh.
That mite not be a bad thing if thats the look that you want though. A bit sort've 'manikin puppety'
Use morphs for facial expressions, eyebrows, nose etc. You can morph things like 'breathing in', by making an 'expanding chest' morph. Or a bounce in his belly, and things like that.
So for all the general movements like walking, and moving arms and legs around, definately use bones.
Personally, i would model him as one object. Make sure you finish him before you add morphs.
Eyes are a matter of individual preference. Bones are a good way, but morph targets can be too.