Actually, it's Stamina that affects movement speed of creatures/NPCs. Hence why when you seriously damage them, and they take a lot of Stamina damage as a result, they slow down immensely. You can also see this with the Fencing Mastery "Pierce", which damages their Stamina by up to 40% of their max Stam over 10 secs. They can be at 95%+ Health then, but 0-10% Stamina, and move slow as hell.
During Pub 97 testing on TC, when the Phoenix would keep it's up to 300 Stamina after tame, they literally could stick to a mounted player at full speed like white on rice. I told my 270+ Stam Phoenix to follow someone that was mounted, and had them try to run away from it. They couldn't. Bleak was there, and saw it. Hence why they capped pet Stamina at 150 after tame. It was to nerf their movement speed down to a more reasonable level.
Pets reach 1.25 attack speed at 150 Stamina. Compare the attack speed of GD at 125 Stamina, against a new pet with 150 Stamina. The 150 Stam pet will attack slightly faster. Back when Rune Beetles could reach 180+ Stamina via Bless, they'd attack at the same speed as when they had 150+ Stam, but would move faster.