What's the difference betweeen Lumineers and veneers? What gives the whitest teeth of the two?

Veneers will be far better to give you a whiter smile than lumineers, since lumineers need to be very thin in order to look somewhat descent looking! even that thin amount of porcelain added can make your teeth bulkier!!
With veneers we are creating additional room for porcelain to mask the discoloration!

 I hate that question because anyone can create a toilet bowl white smile.  Your goal should be a full healthy natural looking smile that provides proper lip support and gives you the shade of teeth you desire..  Value is the term that describes whiteness and Chroma describes color.  White is usually pretty awful what you want is a high value or whiteness to appropriate chroma.Imagine having a can of paint and starting to add white paint.  You will get whiter and brighter paint but the underlying chroma will remain the same.I suggest you start with provisional that you wear for a month or two before cement veneers.  Most patients who get "Whitest teeth possible" end up hating the look and replacing them.Smile creation is an art!  Find an artist who has an excellent local lab who can customize veneers.The brand of veneer is not what determines results.  You never want to see a dentist who only utilizes on brand.  Its like working with a contractor who only uses a hammer.  Ira L Shapira DDS, D,ABDSM, D,AAPM, FICCMOChair, Alliance of TMD OrganizationsDiplomat, American Academy of Pain ManagementDiplomat, American Board of Dental Sleep MedicineRegent & Fellow, International College of CranioMandibular OrthopedicsBoard Eligible, American Academy of CranioFacial PainDental Section Editor, Sleep & Health JournalMember, American Equilibration SocietyMember, Academy of Applied Myofunctional Sciences

If veneers are done properly, there is total control over the shape of the final teeth. With Lumineers you are slightly less limited in the way you can shape the final result. That being said, shape is infinitely more important than color. For that reason, a traditional veneer is usually a better option. Once the shape is designed well, getting a white color is the rather easy.
Best,