It really is a tricky question, on one hand lighter recoil allows for superior, faster follow up, yet at the kind of close ranges you will be using a buckshot load, relying on one good hit might be the best, or sometimes only option. In self defense, overkill does not exist, stopping the threat is all that matters. You're never quick enough and never hit hard enough, so we are back to the endless classical dog chasing its tail of "recoil vs. power". In truth, both loads have a valid argument, and it is up to the shooter and gun as to which you see as advantageous.
Personally, I think that the power argument is absolute the correct one. With shotguns you are relying more on one or two carefully placed shots, and it is more important to make sure your devastating weapon devastates. You choose the shotgun for its hard knocking, hard hitting, hard killing power, don't gut it out, because that is the entire advantage and point of the choice of weapon. You don't buy a 5 ton truck and start putting lighter duty shocks on it, so why do you want to shoot light loads out of a defensive shotgun? If you want a lot of quick, easy, low recoiling follow up shots, stick with your carbine, otherwise, stick to the big rounds for the big gun. You start taking a pellet and 150 fps out of a 9 shot full power buckshot load, and you really don't have the same thing.
The argument that it is as effective is very complex. At longer ranges, buckshot, as well as all birdshot, starts to see an evening out of energies as range progresses. The difference between a pellet of #4 buckshot fired at 1350 fps and 1200 fps out of the muzzle might come very close to even at 60 yards. Some hunters don't mind lower velocities in order to raise pellet count, i.e. low velocity 15 pellet 00 buckshot in 3 inch 12 gauge magnum vs. the higher velocity 12 and 9 pellet 00 loads. Factory 3 1/2 inch magnum 10 gauge shells with 18 pellet 00 buckshot has been 1150 fps, yet has been a time proven, well regarded hunting load. Are you getting the extra power advantage at hunting ranges from higher velocity loads vs recoil? Ask people who do it and see their answers.
That being said, at close range, the velocity does matter, because the short range means very little speed/energy bleed off, so you get your recoil and money's worth out of the heavy load. When you hit an attacker, or anything else for that matter, at very close ranges, with a direct hit with a shotgun, especially full choke, they get every last bit of hate you put into that shell. Apples to apples, you do hit any bad guy harder, and always better, by choosing the faster, higher energy load. This is why full power is recommended, because you can slam the attacker harder, get your full worth out of the big bore gun you carry. Shotguns, unlike pistols, have enough "whump" to stun and knock back things (no not through plate windows, or throwing people back 5 feet like the movies). Heavy shotgun loads can "shove", "heave", and shock someone. People may not know if they are hit in the torso with a handgun round, but nobody will ignore being hit direct center mass by a 1 1/8 oz load of lead at 1350 fps. If you take enough heat out of the load, you lose this critical advantage.
Hammering down weight is the worst of all things. Shotguns are useful at close range because they throw a lot of lead, a lot of pellets, a lot of mass when talking of birdshot at extreme close range. With tight, full choke patterns and close range, shotgun rounds will always hit like slugs, and at are full effectiveness. Taking down the weight kills this slug like effect slowly, till the load is too light to be effective. When talking of individual pellets, its simple to understand that less pellets mean less holes put into an attacker. Experienced hunters tend to shoot heavier loads of buckshot, because there really is never a big enough piece of buckshot, or enough pellets of it. That extra piece of 00 that you left out in the 8 pellet reduced load might have been the one to fly wild into the attacker's aorta putting him out, and where are you without it?
As far as LEO's are concerned, high power buckshot is the best choice when considering barriers and obstacles. If using a buckshot load against a criminal in a car, or other means of reducing the bullet's energy towards the target, the extra energy/velocity in those pellets never hurts, once again.
As far as buckshot size goes, I've heard and seen things that suggest that 00 has become a standard for good reasons. #4 may work in a pinch, and can be very effective at closer ranges, it is small and light enough to fail in some circumstances, especially with range and barriers. At a mere 21 or so grains, it can easily get deep enough in many circumstances at close range, yet might easily fail in the most extreme and unusual ones. Add a little bit of shot angle and distance, then some lower velocity, the buckshot might not be able to hit deep enough to kill. #1 is a much better choice, especially for those considering the 20 bore.
I've probably gone on too long as it is, but I'll wrap up that there is a lot to think about. Depending on you, your gun, and other choices and circumstance, there are a lot of options and advantages/disadvantages. I myself have been tinkering with the 10 bore lately for fun, as a hunting gun for all sorts of things. But, as I've made my own reduced loads, 15 pellet 00 around 1200 fps, I've found that my BPS 10 pump kicks less than 9 pellet 00 out of my 12 gauge pumps at higher velocities. Not sure if I'm going to press my big bore shotgun, too big and heavy perhaps, into self defense, but it provides the last tip; consider a heavier gun.
I actually have a 12" LOP stock on my 870 because it's the only way I can work the action without doing a goofy impersonation of a chicken. 
