In games with an AH system I've noticed that not many players sell their items at very low prices, so items don't get snatched away by other players who then put them back on the AH for much higher prices.
Instead the player who has the item can easily tell by the AH what the item is roughly worth and their listed price will only be affected by how soon they want to sell it: just a little under the cheapest AH price for a fairly fast sell; around the average AH price for a more long-term sale.
In the case of shops I've seen many players who have little idea what their items are worth, and some other players with more knowledge about that will take advantage of it by constantly go from shop to shop and buying up the items that are listed too low. Smart and active players can make huge profits that way on the back of other players. 
Also monopolizing items is easier in shop systems than in AHs. Active players will go from shop to shop to look for the specific items and a lot of trading is done without the rest of the player base being aware of it. The fact that without an AH system the shop keepers have little way of telling how much a rare item is actually worth will play into the hands of the player who is trying to monopolize a certain item. Players will only become aware of a monopoly when it has already there... 
There is a way to include both systems though. Have players' shops exist throughout the game, but also have an AH system where all these items are also displayed. You can choose to view all the shops' items in the game with the AH system and buy them at a slightly higher value, let's say 10% more.
That way players will be able to buy a much needed item without having to browse every single shop in the game only to find it in a shop 5 cities away. This will reduce a lot of the frustration over not being able to find items.
And players can tell what other players are selling the item for, so it prevents other players from abusing possible lack of knowledge about the value of items on the seller's side.
Going to shops can still be beneficial to get items for lower prices, but it's no longer a (sometimes frustrating) necessity. 
The reason why in AHs prices are not far off is that sellers set their prices after consulting previous sales listings or according to the average price others ask. But that doesn't mean that all (or most) sellers know the real value of the items they're selling - they simply use the other's prices as guidance.
This is also the reason why controlling an AH is easy: everything is listed in plain sight (and in real time). You can buy everything that pops up for cheap and sell it seconds later for more. You don't have to go through countless player shops, you don't need to waste a lot of time fishing for good offers, you just hit the refresh button and keep buying/selling.
If the AH has a bidding system and not just a straight selling mechanism, then things get even more interesting because you can really drop or up the prices really fast: let's say some players are selling a similar item for a certain ammount of gold. You place several bids for each item for let's say half the price. You win the bids. Next time someone that wants to sell such an item and checks the previous transactions list will set their price according to your low bids because they see and think "that's the price ppl actually buy for". Then you can bid lower again and drag the price down even more, or maybe just for fun place some high bids on a bunch of useless items and see the prices go through the roof because ppl will think "there must be a good reason why someone buys that item for a lot of gold" ...do you see now what's the problem with the AH system? 
Now let's say I want to do the same thing in a player shop system; I place my shop(s) with outrageous prices - ppl go by, check the prices, walk away (usually ppl buy after going through most if not all the shops to make sure they're not getting ripped off). After visiting a few more shops they can see I'm trying to scam ppl It takes much more effort and coordination to control such a market.
In the end, no matter the trading system, it's all down to 2 things:
1. the items that will ultimately dictate the prices and which will be used as criteria for pricing everything else are the cash shop items (providing these will be tradeable) and/or the real cash to gold exchange rate (providing this will also be available). Usually the demand for cash shop items is far greater than the offer because gold and game items gradually pile up, while the stuff bought with real gold is only sold by few.
2. if you want to become successful you need to have deep game knowledge: knowing most of the items (if not all), how to obtain them, what is the demand for 'em, what's their real value. If you think you'd manage to score big simply by monitorising the AH...well, good luck with that - you'll sure need it
