I think it all depends on what/where you are moving...... if you have expensive and exquisite stuffs, then better to get a more reputable ones with sufficient insurance coverage and professional equipmetns and expertise to move those expensive stuffs. If its just boxes of clothings and sofa/dining tables/chairs etc, then a normal one will do.
Its a very competitive market out there but make sure you have a confirm quote from the mover listing all the 'big' items, its a norm for them not to move items not listed and would often demand extra moving fees....... cheers!!