Advantages to quotes from Lowe's/Home Depot vs direct from contractors?
HD and Lowes to my knowledge do not have any contractors on staff.  Meaning that they outsource all of their services to local contractors.  

Pros


you get a warranty from a company you know will probably honor it in a year
you can sometimes - not all the time - use their financing and may be able to have zero interest for a year if your credit is good enough (if you don't pay it in that time you do pay back interest)
edit:  Adding in another pro since I forgot about why I have used them going back 15 years ago.  During one of my flips I couldn't find a licensed plumber - well I could but I was new to flipping in the area and was under an immensely quick timeline, so the bids I was getting were high but the worst part is no one would guarantee a deadline.  I got a 4k plumbing bid from bigbox but stipulated that it must be done within 10 days or money back.  I couldn't believe the supervisor at bigbox signed it... Day 9 they were 20% done.  I called and informed supervisor and took pictures (with a real camera).  4 plumbers finished the next day.  I doubt bigbox was worried about the job but sure the supervisor was worried about his.  But if you can get them to agree on timelines it is probably very easy to deal with your credit card company to decrease amount.


Cons


HD/Lowes make money by jacking up the normal price by 20-100%.  I have seen very simple small bathroom installations get 20k quotes.  Just thinking I could do 20 of these a year and live very nicely just by doing bathrooms.  
They do very little to vet out contractors.  Usually these are guys who aren't drumming up enough business on their own.  For the bigger companies that HD/Lowes deal with you aren't getting their best people.  The only thing that HD/Lowes does is take contractors off their list once they have had issues.
you will now have a middle man to deal with that will be fed part of the information/issues from you and part from the contractor.  Also you will have to deal with admin issues with the middle man.  I have seen many times HD/Lowes mess up these small contracts and leave something off or promise something to one side and not the other.
you could have multiple contractors for a seemingly easy job.  There is no one "owning" who is going into your house.  
Good luck taking one of the big boxes to court if you can't resolve an issue.  Most of their small print would probably make you file hundreds of miles away and moves things out of small claims.  You are also dealing with a legal team.  Back in the day I had a friend who was using one of the "orange" ones to sub subcontract... He had several disputes.  He basically got a letter from their lawyer banning him from their stores after he filed a police report.


My advice.  I would only use them if you feel that you don't have any reputable businesses around you that can do the work (not reputable Joe from craigslist - and nothing wrong with using Joe if you are confident on what you need to do) or if you feel you are just the type of person everyone takes advantage of.