As a whitebelt, I'm no expert on these sorts of things, but it seems to me that there are few, if any, valid arguments for starting this thread in the UFC forum. That being said, wrestling enthusiasts ought to take advantage of the fact that this thread exists and is getting a lot of hits on the site's biggest forum to clear up a few points that are understandably hazy for the general public.
First, the type of wrestling you would see in high school gyms dotting snowy Midwestern cornfields/Pennsylvania steel towns/whatever is not the same as the types of wrestling you would see in the Olympics (or in gyms in Dagestan, Tehran, or anywhere else in the world). The former is called 'Folkstyle Wrestling' while latter two are called 'Freestyle Wrestling' and 'Greco-Roman Wrestling'.
What are the differences between these styles? Let's first consider GR wrestling. From a very macro perspective, we can simply say in GR you cannot use your legs (or your opponent's legs) as offensive or defensive weapons. No double-legs, trips, etc. are allowed. Moreover, you must accompany your opponent to the ground (i.e. you can't throw him and then sprawl on top of him). In both Freestyle and Folkstyle, legs are fair game. This point isn't fundamental to TS's original post, but I think it's basic grappling literacy (which is helpful when discussing MMA generally).
The differences in Freestyle and Folkstyle are a little more difficult to spot for the casual observer, but these differences cut to the core of what TS originally asked. The biggest difference (IMO) between Freestyle and Folkstyle is the scoring systems. A common refrain is that "Freestyle emphasizes explosion while Folkstyle emphasizes dominance." This is absolutely true but can be a little difficult to understand if you're not already familiar with both sports. What this saying is trying to point out is that the two sports' scoring systems reward fundamentally different types of moves and strategies.
The first thing we ought to recognize is that the match score is accounted for at different times during a freestyle and a folkstyle match. In freestyle, round scores are noted and then reset at the end of each of the three periods. Whoever has the higher score at the end of the round wins it and gets a point. The first wrestler to win two rounds wins the match (barring a technical fall [gaining a large enough point lead in a given round for the ref to stop the match in your favor] or an actual pin). Contrast this with American folkstyle wrestling, where the score is never reset. If wrestler A kicks wrestler B's ass in round 1 and then slightly loses to wrestler to round 2, he still has a lead in points in folkstyle (like winning a 10-7 first round and then losing a 10-9 second round in MMA). This is where the 'Folkstyle emphasizes dominance' part of the aforementioned saying comes from.
Where does 'Freestyle emphasizes explosion' come from, then? It comes from the way the two sports view top control/riding time. In Folkstyle, top control is paramount. At the highest levels of competition, the time differential between your riding time (the time you spend in top control) and your opponent's factors into your final score. For every minute more you spend in top control, you get an extra point added to your final score. Therefore, in high-level matches, where points are hard to come by (since everyone is so good at defense/scrambling), the most surefire way earn points is to stay on top and accumulate riding time (as long as the ref doesn't think you're stalling, in which case you can lose points!). In Folkstyle, there is little to no incentive for the bottom man to LnP because he will get beat up for however long is left in the round (I guess you could say a guy with a huge lead might just stall out the end of the third round, but that's a super risky strategy since you're playing with a possible DQ). This is not the case in Freestyle. In Freestyle, once the match goes to the ground, the bottom man is encouraged to stall. If he can nullify the top man's offensive game and remain flat on his stomach for some period of time (15 seconds? I'm not a freestyle expert.), the match is reset to the feet. Hence, no incentive for riding time. Also, in Freestyle every time you can make your opponent's back touch the mat (even for a fraction of a second!), you get a point (in folkstyle you have to hold a guy down on the mat for at least one second, and you have to reset your grip before you score points for the same move). So quick turns and rolls are far more useful to the top man in Freestyle than working for a cradle etc. Pulling off a lot of moves in succession is also better in freestyle because the risk/reward is far better than it is in Folkstyle (where screwing up would mean potentially losing top control and might even mean ending up on bottom).
What does this say about wrestling/fighting styles? Since Folkstyle wrestlers can remain on top indefinitely, they can then proceed to grind their opponents faces into the mat and attempt to crush their wills by wearing them out. This mentality becomes deeply embedded into the minds of American wrestlers. The mentality, simply put, is to suffocate your opponent and make them quit (i.e. exert total dominance). There's a very clear progression from American folkstyle to Fitching (not a problem in my book but I can see why some might not find it that exciting). What TS might think of as 'boring' wrestling stems from a philosophical decision made about how American wrestling is scored. On the other hand, the more 'exciting' Russian (or, more accurately, 'international') wrestlers come from a tradition that places greater emphasis on motion. Take the guy down, throw him, whatever, but don't settle for doing that once. You've got to keep moving because round scores only matter for one round. I could see how this type could lead to a mindset that forces action a little sooner in the match.
I don't think you can see either type of style is 'better' absolutely. Russians have produced better Olympic wrestlers (Satiev > Smith, Medved > Baumgartner, Karelin > anyone), but as others have said, I have to think at least part of this is the fact that Americans largely don't train folkstyle. I'm not trying to do a nationalist pissing contest thing, I just think that's an unassailable fact. If Smith, Baumgartner, and Gable had trained freestyle their whole lives, we may have a different story w/r/t to the above comparison. Hell, if Gable and Smith could just have been convinced to stick around international wrestling for longer than they did, we may have a different story (they were damn good anyway, but never had the long-term dominance of the state-sponsored Russians). I hope this post was somewhat helpful (I admittedly oversimplified a lot things but saw that this post was getting out hand, length-wise). If not or tl;dr, flame on, I guess.
