Cardboard is generally cheaper, but plastic totes are much more durable.  Better withstanding impacts and weight while being able to be stacked easily makes them ideal for protecting fragile valuables in your move.

Overall yes recycling is good for the environment as it reduces waste and saves energy.  Did you know it is the most recyclable item, but only if it is actually recycled.  Usually it ends up in landfills and while decomposing it releases methane.  Methane is a greenhouse gas that is a contributing factor to climate change.  

It is considered bad due to the fact it isn’t able to biodegrade easily.  But in this case these totes aren’t going to be tossed into the garbage or a landfill unlike the chances are with the cardboard boxes.  These totes will last a long time and in a way are being recycled with every move that they are utilized for the next customer.