When you ask this question you are going to get 99% opinion because it is completely subjective. Plenty of people out there (like myself) absolutely hate multi-FX rigs, while others swear by them. There's no real scientific reason to pick one over the other, but here's a quick match up between their basic features:
Pros: Takes up less space; less expensive than a comparable pattern of boutique pedals, potentially easily configured depending on how intuitive the user interface is, most are software driven, easily powered with a single cable, no capacitance loss across longer cable runs, sometimes easier to use during a gig, most can midi sync with a click track, a single master volume (very big pro here). Good for guitarists that like options and swap between them a LOT.
Cons: Digital, can be annoying to tweak, hard to get some more unique sounds out of them, lack dynamics of some more high quality boutique pedals--specifically overdrives, tend to be very opaque.
Most all-in-one's sound obviously digital. Even the best modeling software out there is hard pressed to emulate analog circuits properly; it's tough to accurately represent hardware in software in many applications, and lots of these systems don't have the computational horsepower to compute the real deal algorithms quickly enough (Fourier transforms are hard, even the fast kind :D). Some people consider this to be a con, but others like the crystalline sound that you get from a purely digital source.
Pros: Endless configuration possibilities (this one before that one, etc), more tangible--think of playing with legos vs. configuring sounds in software, arguably more versatile than some all-in-ones because there are a very large number of pedals on the market each with it's own sound, analog sound, digital sound, whatever sound you want, more modular. Good for guitarists who have a settled on a single sound and want to run with it, although a multi-FX unit could provide this same functionality as well if you don't monkey with it much.
Cons: Suffer from capacitance loss across long patch cable runs, way way way way more expensive, but scalable to the users budget, have to deal with inconsistant levels across the board if you have multiple pedals with volume controls, you have to compensate for amp goosing (boosts), potentially less compact than an all-in-one if you have a lot of pedals.
I prefer pedals due to their modularity, and my board is arguably more configurable than any multi-FX rig out there, I just gotta have the scratch to purchase that new cool pedal I want. Note that this only barely scratches the surface of this topic. Many a guitar forum has spent hundreds of pages discussing this exact issue.
I submit that there is no right answer for this conundrum :D.