Cast iron is a classic, sturdy and long-wearing. It will retain heat better. It's very heavy though, and may cost more to purchase and install. Acrylic is lighter, and to my mind, a flimsier and cheaper alternative. Given the choice, I'd select cast iron every time.

I would also go a cast iron tub because they are the best! They are much easier to keep clean than an acrylic tub as well.