I have concluded a couple of things when it comes to buckshot from a 12 gauge, but your mileage may vary. When I talk about buckshot patterns, I am referring to 40 yards, for deer hunting:

1) the smaller the shot, the denser the patterns I tend to get. (Though that Trulock choke I mentioned above did tighten up 000 patterns pretty significantly.)
2) more pellets doesn't usually result a denser patterns, but usually results in an equally dense but wider pattern with more fliers. USUALLY.
3) moderate velocity, around 1100 fps (or less), loads tend to pattern better than high velocity loads when the pellet sizes and counts are the same. (For instance, Federal 3" 15 pellet 00 at 1100 fps consistently patterns better than Winchester 3 1/2" 15 pellet 00 at 1450 fps.)
4) most aftermarket buckshot choke tubes aren't any better than an OEM flush choke of the same constriction. In fact, they tend to pattern worse. The Trulock choke above is the only exception to that rule I've seen.
5) the bigger the shot, the better it patterns as the choke opens - to a limit. When it comes to OEM flush chokes, 000 and 00, for me, tend to pattern best from modified to improved modified. 0 has done well with a full choke. And #4 patterns well with full and slighlty tighter. In fact, I get my best #4 patterns from a .685 X-Full turkey choke (in a Browning Invector Plus barrel.)
6) 10 gauge guns pattern 00 buckshot better than 12 gauge guns.

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