What are some of the common materials used for bathtubs and is there any material which is significantly better than the others?
In Singapore, there are 3 very popular materials:
Cast Iron
Acrylic
Solid Surface
Cast Iron Bathtubs
These bathtubs are moulded from iron and the glossy white surface that you see is given by a thick layer of porcelain glazing over the iron bathtub. They are easily recognizable by a light bluish, metal underbelly.

These cast iron bathtubs are best known for:
Durability
Sturdiness
Easy cleaning due to glazed porcelain finish
However, if the porcelain layer gets chipped, the underlayer of exposed iron might possibly rust so do be careful around these tubs. They also tend to be cool to the touch and a little noisy.
But the sturdiness of the bathtub more than compensates for some of it's downsides. They look extremely beautiful in high-gloss. They also have the "solid" look if that is what you like.
Because these cast iron bathtubs can get pretty heavy, they are typically only used for built in installation type of situations.

Acrylic Bathtubs
Bathtubs made with acrylic are highly popular now because they are easily formable into many shapes and sizes. Hence, they are widely used by manufacturers to make the modern, clean cut designs we love.

They are easily recognizable by the coarse matted under belly and are warm to the touch.

Acrylic bathtubs are:
Lightweight
Relatively inexpensive
Surface is repairable for minor chips or scratches
Durable
Be warned not to use abrasive cleaning agents or tools. They could scratch the surface and the bathtubs will lose their glossy surface protective layer. It will still remain functional as these bathtubs do not rust but we all want them to look great for many years don't we?
Solid Surface Bathtubs
Solid surface material bathtubs are gaining popularity in the market. They have all the advantages of the stone bathtub and more. The extra smooth, tamed final finish is easier to manage for maintenance. Because they are not as heavy as stone, there is also less consideration for floor loading issues.

Solid surface tubs are:
Resistant to corrosion, swelling, scratch, stain, heat, chemical and moisture damage
Durable
Safe and sturdy
Completely homogenous
Thermoformable
Able to re-surface
They can be highly costly relative to bathtubs of other materials. For floor loading requirements, you have to note the weight of the tub + water capacity + human weight.
In conclusion...
As with all products, be wary of low quality items. They could be made of the same materials but when it comes to durability and design, they just can't make the cut. Some materials if made in low quality may even be toxic to our bodies!
There are of course many other types of material on the market like fibreglass; steel enamelled; stone; cultured marble and even glass. Each have their own set of characteristics. So go ahead and research more before setting your heart on a bathtub material and design.
Now follow this link to see design inspirations for bathtubs. Enjoy!