The advantages are generally better control over your recipes and the ability to make beers you otherwise couldn't (those that require adjuncts that must be mashed with a base grain). Additionally, you gain very fine control over the fermentability of your wort by being able to control the amount of crystal malts in your beer, mash temperature, mash length, mash pH and mash thickness. It really allows you to develop a brewing "style" that fits you.
Cons? Your brew day will be about twice as long, if that's a con for you (I cherish my long brew days). Also, you need a bit more equipment, as you need to move off the stove and onto a burner/pot that can boil 7 gallons of wort comfortably, but that's about all you need. If you want to do the BIAB thing, just grab a bag and that's it. You can do the cooler mash tun if you want, or build a crazy HERMS/RIMS system with full automation if you want. It's all about choice and your brewing style.