The answer to your question is found above but can be summarized like this: You can use an ER chuck to hold most parts but you especially need it on thin walled, finished or threaded parts to minimize damage to them. A 3 jaw chuck is otherwise faster and accurate enough for first operation turning. A 4 jaw independent chuck is potentially more accurate but takes longer to dial in.
An ER-40 (vs an ER-32) simply allows you to clamp bigger stuff, up to an inch OD.
As to accuracy, it really depends on how accurate your spindle is, how accurate the chuck/collet/nut assembly is when sitting on that spindle and finally, how accurate your part is. If you're going to use nominal/rough stock then an ER collet offers few advantages, speed not being one of them (5C is faster). If you are working with ground or an already turned part then an ER collet is a good choice ... in other words, second operation work.
I have 6 high-end jawed chucks, two ER chucks and one magnetic chuck for my lathe. The most used, by far, is a good 3 jaw chuck. The least used are the magnetic and ER chucks.