What are the similarities between the two books, The Remains of the Day and The White Tiger. Both very different but any similarities?

Yes, the two books are very different, but there might be
a similarity in the protagonists.  Both Stevens and Balram in The Remains of
the Day and The White Tiger respectively are looking for
ways to be better at their jobs only to eventually realize that they work for less than
reputable men.  Stevens continually asks himself how he can be a great butler, and he
performs his duties with dignity and pride.  However, he later learns that his former
employer Lord Darlington was involved in spreading propaganda under Hitler's regime. 
Stevens then questions whether or not his service is respectable under such a man.  He
eventually resolves to try to be of good service to his new employer.  Similarly, Balram
ends up as a driver to Mr. Ashok and his wife Pinky Madam, and at first Balram thinks
that the pair are quite revolutionary because they claim to treat those of the lower
class with respect.  However, Balram later learns that Mr. Ashok is involved in
financial bribes and schemes, and he even blames Balram for the death of a young boy who
was really murdered by Pinky Madam.  Balram resolves to redirect his service to his own
venture and opens his taxi service.