If price shopping for Invisalign is how you decide on a dentist or orthodontist, you may find that you didn't really get the lower price. Fees for services are determined by each office, so you may end up surprised to find that you end up paying more than another office.
If one office quotes $5800 for Invisalign and another $6000, you likely would choose the $5800 office. But that office might charge $600 in addition for retainers when the other office does not charge extra.
The only way to know is to ask each office, but if you are choosing only on price you may not be happy in the end. High fees do not always mean better service or product, but it might.