Perhaps a bit more information is needed ...
- I assume this is slab on grade.
- Are frost walls required?
- What is the use of the space?
Which to use kinda depends on many factors not stated.

Ralph
Structures Consulting
Northeast USA

slab on grade
no freezing area
residential first floor is concrete....or garage slab?...any of those
 

Agree with Ralph, if you want a quality response give us the exacts of your project. If you are asking for general rules of thumb or something, you could write a whole article on this subject. Also depends on where you are in the world...

Generally, in my experience in Florida (sandy, well drained soils, no frost)- thickened-edge monolithic footings are residential or light commercial, two stories or less. I don't like using monolithic footings for higher loading because you have a non-concentric loading condition and differential settlement could result in a cracked slab where the ftg tapers into the slab.

Especially if we are talking about CMU, then a stem-wall type foundation to me is preferable where the slab may float with an isolation joint between the slab and wall. This lets the settlement of the wall occur without possibly damaging the slab and floor finish.

Contrarily, I have seen slabs settle in a stem-wall house without the foundation moving due to unusual soil conditions...

In general, I agree with a2mfk's comments.  I come from an area where frost is a major concern, resulting in perimeter frost walls (at a minimum).  Given this, slabs-on-grade are usually not connected to (and are isolated from) perimeter walls.  On occasion I have seen SOGs connected to perimeter walls to provide diaphragm action.

I'm not sure how you would distinguish the difference between a monolithic concrete slab and a floating concrete slab (if there is no perimeter footing).

As with any SOG, proper sub-base and base material preparation is the key.  Consistent depth of excavation and base material placement and compaction will greatly influence the performace of the slab.
 

Ralph
Structures Consulting
Northeast USA

As chance would have it, saw a copy of an article on a coworker's desk yesterday:
"Should slabs rest on or be attached to foundations?"
Concrete International
November 2010

Depending on the size of the slab, I would assume some control joints are required.  If so it is almost impossible to have the slab joint continue through the enlarged monolithic edge footing.  If unsightly cracking of the slab is an issue you should stay away from the mono type.  

Robert222,

In areas with expanding soil, it is better to separate the slab from the foundation unless you plan to use a structural slab in which case you require a voidformer in the event of swelling soil or frost heave.

Your laconic question and subsequent response do not help very much in describing the problem or resolving the issues which you are facing.  Would you care to expand on the type of soil in your area, climatic conditions and any other factors which might play a role in the issue which you have presented to this forum?

BA

This is entirely dependent on the soils and moisture.

In Dallas, most soils are expansive, with large change in moisture from season to season and during multi-year droughts.  Not unlike seasonal freeze-thaw, we can get inches worth of movement in soil.

Floating and interior slab works fine if you plan for movement, such as under partitions.  So a garage slab could float freely without too much trouble.  Inside a house, you are inviting problems having a detached, floating SOG which is not protected from moisture-induced soil movement.

Sometimes the best course is a raft/mat foundation, but for houses, I find that piers supporting a perimeter wall and the interior of the house is the most stable and economical.

Also, is you have expansive clays, do not over-excavate unless your backfill is dense lean clay and is compacted. Do not use void forms under slabs where the base is below the surrounding grade for the same reason.  I worked on a building with a slab over about 2 feet of loose, granular backfill.  The fill acted as a reservoir for water, resulting in swelling of the underlying clays and raising the interior of the slab in excess of 6 inches over 40 years (just as ongoing plumbing leaks can do.)

I have heard that the perimeter footing could become unstable if you don't don't have the slab attached to the perimeter footing to work as a stiffener/diaphragm.