Purpose built, off the shelf:
+ reviews, you can research and find out what you are getting for your money
+ Tried and tested fit, quality and sound (or lack of!)
+ Hold their value when sold second hand
+ Some level of modularity, matching b pipes with various backboxes etc
- Generally expensive
- Not always great quality, despite the prices
- you are limited to what is on sale.
Custom:
+ You can get exactly what you want, especially handy if no off the shelf item meets your requirements
+ Generally cheaper
+ Can be excellent quality if you go to the right place
+ The ultimate aggressive setups*
- Good places have long waiting lists
- Not worth much to sell on second hand, regardless of quality
- can be rubbish quality (Powerflow!)
*I had some very specific requirements for my exhaust. I had an unsilence B pipe and wanted plenty of volume, and getting a very aggressive tone was key. For this top level of rortiness, you need (imo) and unsilenced b pipe and minimal backbox silencing. Even the "very loud" Buddy Club Spec III has a small centre silencer. I knew I wanted a straight-pipe exhaust (no silencing at all) like a Buddy Club Spec II, but they don't make one for the EP3. I also wanted it to look like it had a jap can backbox with a 4" slash cut tip. At this point, I knew that no off the shelf exhaust would do so I went custom. I had a straight pipe exhaust made with a "sleeved" backbox, so it looks like an angled Spec III but is in effect a Spec II. I got it for what I think was a very reasonable price, the quality is great, though not up there with the ultra-neat stuff like Blitz, but at a fraction of the price I can't complain, I'm super happy with it. The only downside was that after paying my deposit, there was a 7 week waiting list, as I went to a very well reputed and in-demand place locally.
On the flipside, a friend got a Powerflow exhaust for his Fiesta ST, which is basically a franchised place where they download a blueprint for an exhaust for your car from a central database, weld it up and fit it to your car. The quality is dependant on how good the fabricator is, in my mate's case he was not amazing. Solid but aesthetically very sloppy welding, looked like a high-schoolers design technology class build! The sound was not so hot either. I suppose Powerflow sort of bridge the gap between off the shelf and custom, but they have so many designs on their database I'd be surprised if they ever built a prototype of each and every one they had CAD'd up, so you can end up with a poorly designed, expensive exhaust costing like an off the shelf system, with the potential for poor workmanship you would find at a bad custom place.