Swings and roundabouts. It really depends on the model and the time you have and what its for, how close is it going to be seen and so on

its a case of thinking about the topology, will you benefit from extruding say an air intake/scoop on a surface because it is moulded or shall I model a separate scoop with a nice bevelled edge and sit that on the surface so the light pick up the edges...this of course would mean intersecting geometry which is acceptable and for the most part unavoidable. Depends on the detail and the type of design you are doing.

You could build say a piece of footwear like a boot as one object and cut in the detail, or even use dispalcement, or if it is to be a high res boot then I would make it out of say four to five pieces of geo with nice edges and place them all accordingly, so you would have the sole, heel, and then maybe three bits of geo for the upper leather which would consist of the main leg/calf leather, heel leather and finally the main foot area at the mid going to the toes.

So as I said, with all in one meshes you have to think about the edge loops keeping the flow right, no odd geo and bevel to make edges sharp if need be, whereas with separate geo you still need to to keep the geo looking good but if the geo intersects just delete what you arent going to see. Plus the fact you arent going to worry about matching the geo edge for edge and so on...

to cut the mesh though and place the verts and snap them to others is pointless, firstly because it wont render correctly but also you may as well just merge into one mesh.

hope this helps

J