It seems to be replicating a fault common in printing called misregistration, but deliberately for effect.
It happens when printing plates are misaligned, or when running printed sheets several times through a printing press to overprint additional colours, but without the correct positioning settings, or when sheets are misfed into the press by the sheet feeder.
Does it have any cons? Yes. Usually professional printers strive to prevent misregistration. It's seen as a fault.
Does it have any pros? Possibly, if you want to make your work look deliberately faulty. It could be viewed as some kind of allusion to poor quality printing, for a kind of retro/grunge effect.
I'd avoid overuse of this kind of effect, otherwise the danger is that it could just make your work look like a badly printed document. It's OK for a bit of fun I suppose.
I suspect it was probably already made using vector image editing software. There would certainly be nothing to prevent you from using that kind of software to recreate it.