As has been stated before, shape changes the taste of pizza since it usually describes how the dough was formed, round pizzas are frequently rolled & hand tossed (notable exception being round pizza that is cooked in a pan, an abomination in my opinion), while square pizzas are rolled & pushed or the dough is proofed in pan so that it expands to the size of the pan. I greatly prefer hand tossed pizza to pizza that is cooked in a pan, so I generally go for round.
Another reason people notice a difference in taste between square and round pizza is that many small restaurants will serve both round and square, the largest sizes being the square ones. In this case the large sheet pizzas may be half baked and half sauced and put in the fridge until they are needed, this has an noticeable effect on taste & texture.
Also, someone asked about why there is usually a slice of pepperoni in the middle of a round pizza, this is because pepperoni is often put on the pizza in a spiral, and that center piece is either the start of the spiral or the end.
I’m surprised that so many people encounter this. I’ve worked at four different pizza places over the last 25 years and the method was always to position them so as not to cut through them. I remember one place even had a handy diagram showing the proper placement. Also, the only time I’ve seen a round pizza cut into squares is at those arcade type places, a la Chuck E. Cheese, in order to get more pieces per pie.
As to the OP, round all the way. Of course the only square pizza I ever seem to encounter is that thick stuff you tend to find in shopping malls. Blech.