Doubtful it would cause more damage but the damage would be different for sure.

We really don't know what a Zombie can survive but the whole idea of Birdshot is to not ruin the meat and also to increase the spread of the shot pattern making it easier to hit a bird in flight.
There could be hundreds of really tiny pellets in each shell.

So on one of us(most anyway) even birdshot at close range to the face would bill a killshot but these darn Fresh Zombies are pretty tough at least so far.

Buckshot on the other hand is more like standard handgun bullets but more than just one ,they are balls crammed inside the shell tube and with 00 Buck there are not too many(7-9 is typical) thus causing much more damage and as you witnessed at close range pretty much blew Petes head off.

It is pretty common in a defense load with just 2 shots to set them up that way too.

I would carry Buckshot myself or maybe Slugs which are a single huge projectile depending on the range I expect to be trying to keep.

In close quarters though once I realized what I needed to hit the Buck should be the call,maybe even a slightly lighter load with smaller pellets but more of them in the shell.

You also have to consider over penetration where the metal goes right through the target and goes on to hurt something unintended!
There is of course a trade off between shot size and penetration.

 

Point blank all the lead is bunched together. Plus the pressure of the blast. For reference, google 'revolver cylinder gap blast', you'll see how much damage pressure can do.

 

Which it looked like it did to me the first shot too.

Zombies are a pretty unique variable here if you want to get all technical about it?