You're wasting your money on the choke if all you're going to put through it is "cheap walmart bird shot loads". The promo loads and most game loads generally only have ~3% antimony, which means the shot is pretty soft and deforms a lot. They'll also have cheap wads that don't help create a good pattern. A super tight choke may deform more pellets and you end up with a poorer pattern than you would with a standard full choke. Target loads(AA, STS, Gold Medal, etc.) have 6% antimony in the shot, which means it deforms less and gives better patterns. Target loads will also have a better wad.
I'm sure you shoot rifles and handguns for groups, and you really need to do the same with a shotgun. The only way to tell if a load/choke combination perform well is to shoot patterns, observe the results, count pellet holes, write everything down, and compare. You may even find out that your full choke really only gives modified choke patterns with the load it really likes.
40 yards, 30" circle. Pellet percentage inside that 30" circle is what determines the actual choke/load performance.
IIRC:
40-45% =Cylinder
45-55% = Improved cylinder
55-65% = modified
65-75% = full
Pretty decent article on the subject
here