What is the difference between "You will never let me down & you will not disappoint me"?

THE DIFFERENCE BETWEEN ‘LET ME DOWN’ AND ‘DISAPPOINT ME’.
 
With regards to the full sentences that you have written i.e. ‘You will not disappoint me’ and ‘You will not let me down’, I’m afraid these cannot be said with absolute certainty, as you are ascertaining that another person will or will not do something in the future. This is something you cannot predict (unless you have psychic abilities!), thus it cannot be said with such conviction.
You could, however, say ‘I hope you will not let me down’ or ‘I’m sure you will not disappoint me’.
 
As for the specific terms ‘let me down’ and ‘disappoint me’ – in English they are very similar!
A slight difference could perhaps be that LET DOWN is used when a specific promise had been made to someone but later broken, whereas DISAPPOINTED  is more along the lines of expectations that haven’t been met.
 
Examples:
– Sarah said she would go to New York with me, so I booked my flight and now she has let me down!
– I’m very disappointed that you got such low marks in your English exam.
 
I hope that answers your question!