Factory Y pipe is a POS. But it allows a single in, dual out muffler.
A true dual system would not have a Y pipe, but to get true dual you'll need to cut out the Y and have two mufflers and it would still need an H or X pipe to equalize pressure down stream.
Your picture is of a Cat-back system that replaces the OEM pipe after the Catalytic Converters (hence the name Cat-back), using a single in, dual out muffler which does close to the same thing as an X or H pipe in a true dual system.
If its only your muffler that is shot, I'd say look at the Mufflex DIY bolt in kit made up with a single-in, dual-out Mangaflow 14", 18" or 24" and factory equivalent stainless make-up pipe, or the Carven equivalent.
The Cat-back's are nice, but unless your pipes are shot too, no added zoom you can't get with a new direct flow muffler (IMHO).