I think the important point here is that there is not a "one size fits all" solution when adding a bucket grapple. The geometry is important and the mounting is critical both for strength considerations and to determine just how the grapple will close. Unfortunately, most of the grapple sellers are just trying to sell their own model and don't adequately address these various considerations. Perhaps we can use this thread to point out some of the options.
Here is my attempt (note, I own a grapple not a bucket grapple...the following points are more important to bucket grapple choices):
How is it mounted? I have seen several systems. One is to directly weld or bolt it to the upper lip of the bucket. This seems unwise unless you have a heavy duty bucket. A better variation is to weld or bolt a 3/8th steel strenthening strip that is at least a bit wider than the grapple attachment points to spread the load out. Another options (mentioned by 3RRL) is to weld or bolt a 2x2 bar across the bucket top. That would provide not only strength but also raise the grapple arm which can be an advantage. A third system used by ATI (round tube) and Add A Grapple (square tube) is to make the mounts on the bucket sides with a bridging tube that the grapple is attached to. While this may sound awkward, it does give you the flexibility to modify the height of the tube to give you desired jaw closing geometry and also allows you to bridge over the top of any bucket chain hooks that would be in the way of a direct mount. One big advantage of the ATI and Add A Grapple set ups that none of the Ebay sellers has figured out is that you can easily remove the whole grapple in a minute or two by undoing a few pins. Nice feature if you don't use the grapple all the time as the grapple does interfere at least a bit with vision.
How long are is the grapple arm? This is critical as it determines whether the grapple will close and meet the bucket lip or will overbite or underbite. There are advantages to each (see posts above) but it is unfortunately a one time choice you need to make. If there is no compelling reason to choose over or under bite I'd recommend a minor underbite so the grapple contacts the bucket lip just inside the edge. The trade off here is jaw opening width (largest thing you can fit in the grapple) vs. tightly gripping a small object that needs to be pushed back into the bucket for secure loading.
How many grapple arms? If you have a bucket bigger than 60" you could install two grapple arms and plumb them to work together or independently or even as 3RRL has done to work together but self adjust separately. For most utility purposes and especially for buckets smaller than 60" one grapple arm is enough. Most grapple arms are roughly 24"-30" wide though there may be some differences between manufacturers. One arm is plenty to hold a log or a pile of brush but two arms will allow more flexibility in grabbing odd shaped loads and allow you to grab piles of brush without thinking as much about making sure you have a good grip on the load. Some full grapples have grapple jaws of equal length (WRLong comes to mind) and that would be an advantage in most circumstances. I haven't seen anyone selling a bucket grapple that is as wide as 48" however (but that might be a nice idea).
Teeth vs no teeth. For brush removal teeth are nice because they help hold brush in the jaws especially before you close the grapple. That adds to the effectiveness of the grapple in ripping vines out of trees or snagging bushes when loading. However, it also means that the teeth can more easily become entangled in thorns etc so unloading is not quite as smooth. Teeth also give the grapple an edge in holding on to a log though the jaw pressure is generally enough.
Hydraulic cylinder placement: Generally the cylinder is mid grapple and this raises some issues with debris being able to pop through the grapple teeth and potentially damage the cylinder itself or more likely snag the hoses. At least one manufacturer has put in a protective plate to hide the hoses and cylinder behind. While that seems reasonable it does have the down side of obstructing vision pretty badly. If I had my choice I'd have a thin armoured strip just a bit wider than the cylinder and would securely run the hoses behind it so they are out of danger.
Hydraulic controls/hook up: There are a number of recent threads that go over the pros and cons so I won't repeat those points in detail. Basically you can use one of several types of diverter valve off the FEL hydraulics or use rear remotes. Diverters are popular but will cost about $500 more than using rear remotes if you already have them or just a little more expensive than installing rear remotes and adding hoses to the FEL/grapple. There are kits to install diverter valves and these seem to take about an afternoon to hook up. To use existing rear remotes you really just need the right length hoses and it only takes 15 minutes to get up and running. With a joystick mounted diverter button you use your thumb to change the curl/dump function to open/close grapple. With the rear remote you slide your hand back off the FEL controller to the fender mounted rear remote valve handle and do the open/close that way. I use the rear remote system and am perfectly content, others like the diverter valves.
Others may have additional pointers. I will close by saying that my 48" Millonzi grapple (not a bucket grapple) is right up there with my bush hog as the best implement I own for brush clearing. Just for discussion sake I'd say that if a bucket is worth about two men in brush clearing then a bucket with toothbar would be worth about four. I'd guess a bucket grapple would be worth about 8 on that scale and a full grapple maybe 12-16. The value is not just in being able to transport brush/logs but also in ripping them out of densely packed areas where a man could not get access easily. If you run a FEL into thick brush until you almost stall, you can rotate the bucket down (dump) and clamp down on the compressed brush then reverse and pull the whole mess out. (When there are a lot of vines I raise the FEL with open grapple and advance into the tree then rotate the grapple, clamp and lower the FEL which pulls the vines right out.) I do that and then back out about 20 feet, drop the load in front of me then drive right over it with my bush hog on while I go back for another load. Finally I turn the tractor around and back into the denuded area with the bush hog. Amazing efficiency compared to doing it by hand or without the ability to grapple especially in thick thorny brush or with overhanging vines.
Photo attached shows in background the type of overgrowth I am clearing with the technique mentioned above. The cleared areas were just as dense as the uncleared areas an hour earlier. The deer came in to the area while I was working and I am still figuring out how to catch him with the grapple
.