This might be lengthy but I hope it has some valuable info to help you and others that consider these tools.
I did, originally, look into the tool that you showed. I found a couple different ones online that I considered. I bought a similar item called a "Target Buddy"
http://www.targetbuddy.com/ It is a pretty effective tool but is pretty bulky. I have only used it around my yard and, as for the holes that it leaves, I think it is good as you can't tell, when I am done, that I even dug something. Only exceptions were a couple places where my pinpointing was a little off and I had to make multiple adjoining holes to find an object. After piecing the plugs back into the holes, there was some dirt between the plugs. Not bad though. If you are careful and all, you would probably be OK. I would still be cautious though of using these types of tools in other peoples yards or the park etc. You really need to be careful when digging on public property or in other peoples yards. Especially if they are well maintained and manicured.
One thing that others cautioned me of and I would agree, is that you want to also be careful not to damage your target. Don't just plunge your plugging tool, or any tool for that matter, into the ground. Be careful and more deliberate. I found that it isn't as hard to do as you might think. The edges of these tools are obviously kind of sharp to cut through the sod. They can also scratch your treasure. I found a penny with mine, the other day. When I pulled it out of the plug, there was an obvious fresh set of gouges on the face of the coin. Fourtunately it was a common modern penny.
I posted in another thread some things that I learned while putsing around in my yard. If you detect an object that is, according to your detector, an inch or two, Odds are it is right under the sod. Pinpoint the best you can and use your trowel to cut a small slit in the turf. Feel under and see if you can locate the object and pull it out without digging. A lot of items are right under the sod. If your detector tells you that the object is about 3 or 4 inches under, you might want to cut a flap out of the sod and carefully fold it back. Then, using a trowel like the Lesche Predator,
http://www.predatortools.com/products/85E.htm carefully probe and dig around to find the object. You might also want to have a pinpointer handy at this point. I use a Whites Bullseye II.
http://www.whiteselectronics.com/bullseye2w.php
With a pinpointer, check your hole and see if you can locate where the object is. I like the hand held pinpointer, as opposed to my regular detector because it is easier to handle when I am on the ground digging. Don't have to get up and then kneel down over and over. The Bullseye II like other pinpointers, can be set to only detect things that are an inch or two away. That way, you can run it along your hole and know exactly where the object is. Hold it near a coin and while pushing the button, turn the sensitivity knob till you get a beep at a distance you are comfortable with, I usually set it to beep about 2" from my target. I also like that it has a vibrate mode so you can dig more discretely and it will vibrate rather than beep. Also it has an LED light that will illuminate inside your hole. Then, after you have retrieved your target, place the dirt back and put your plug back. Remember when digging a flap, cut deep enough so it has plenty of dirt on the underside of the sod. One thing that I hear about happening frequently, is that detectors will go to the park and dig good holes and flaps... They will put eveything back carefully and cleanly and later will learn that all the flaps and sod had been removed. Sometimes, animals, (dogs, racoons, squirrels...) will smell the fresh dug earth. Their instinct is that another animal burried some food there. So, they dig it up. Thus why the pluggers would seem a little better. Much more of a challenge for an animal to dig up. So, I think the only real solution to this is to make sure your flaps are deep enough to hold well. Not something that someone will trip over or some small animal will yank up.
Now, if your target is deeper, say 4 or 5 inches or deeper, that might be where your plugger would be best used. Take a plug out of the top and check it with the pinpointer or your detector. Take a good quality plastic plate or bowl with you that you can put your dirt and plugs into. That way you won't make as much of a mess and you won't loose much of your dirt around your hole. You can scan over the plugs and dirt, in the bowl, to make sure the target isn't embedded inside. If nothing is in the bowl, check the hole again with your detector and make sure your target is there. If the detector still reads something, set the first plug, (the one with the grass) asside carefully and then check your hole with your pinpointer. Check the sides and the bottom and use a trowel like the Lesche and dig the bottom and sides. The other day, an idea came to me. I might go out to Bed Bath and Beyond or Linens and Things... and get a ladel like you would use in your kitchen. Something with a decent handle. Maybe plastic end to it so as not to damage a target. After loosening dirt in the bottom of these holes with a trowel, using a ladel to scoop out the loose dirt would be good. Make things cleaner as far as dirt on the grass goes. Odds are, your object should be somewhere near by. If you still don't find your object and it might be deeper, you might take another plug out of the same hole if you can. I am guessing that my "Target Buddy" is about 4 or 5 inches deep. Based on the length of the handle, and my experience, I can take two plugs out of one hole before I max it's depth. I should be able to get a max depth of 10", I think. By now you should have found your object. Return all the loose dirt to the hole and replace the plugs. Place the grass plug in last, of course. If you keep the diameter of the hole the same as what you get with your plugger, when you have filled everything in and replaced that top plug, you shouldn't be able to tell you were there.
I don't know about the plugger that you showed. I looked at it and the "Target Buddy" and decided on the later as it seemed wider. Pictures are hard to judge though. From my experience though, the "Target Buddy" offers a hole that is plenty wide to put my hand into. I have fairly large hands too. My thought was that it would make it less likely that I would have to enlarge my holes and do further damage. From the little work that I have done with it, it seems adequate to be able to, as I suggested above, take out a plug and dig along the bottom and the sides of the hole to widen out ( upside down cone with wide on the bottom). Then refill and replace the top plug and leave little damage.
Not sure of the shape, where they can piece geometric plugs together to cover larger areas. From what I read, the key is to make sure you cut deep enough and leave enough soil under the sod. I am not sure if it has to do with cutting a complete circle as it does stripping the sod too shallowly off the ground. I would always, even if the target on my detector is 2" take a full plug out. Although, if your target is that shallow, like I mentioned above, you would be better just cutting a slit in the ground and probing for the target. You shouldn't take a shallow plug, just like you want to be careful to not cut your flaps too close to the surface also. You should plan to only take a full plug. That would be 4 or 5" deep with all the soil attached. If you find the target, remove it carefully. Don't uneccesarily crumble all the dirt away from your plug. That is where the roots are and if you cut too shallow or overwork all the soil away from the grass, you will damage those roots. It is better to drop a 5" thick plug back in the ground, rather than one that is only an inch or two. When you do replace your plug, make sure to tamp it or press it down good to make sure the roots get good contact with the soil that surrounds the plug. It can take longer for the roots to recover if they don't have adequate dirt under or around them. Soil left also retains moisture and protects the roots from the heat and drying of the sun. I really believe that is the source of most of the problems. Another thing that one should condiser doing, whether cutting a 3 sided flap or a plug. If it is dry and there is not any rain in the forcast, don't dig. Or if you must, carry a bottle of water around with you so you can water your plugs in. Also, avoid plugging in the middle of the afternoon or on hot dry sunny days. I think it was discussed one time before, Take a bottle of Cayanne Pepper with you also. Sprinkle it over and under the plug to deter animals from digging up your flaps and plugs. 
