Both Testing's are important because, 

equivalenc partitioning is used to define a type of input 
object (test data) 
example

          valid            invalid
          A to Z           Special charactes  
          a to z           Blank spaces.
          0 to 9
Boundary value analysis is used to define a size of input 
object (test data)
example,  input object should be in between 4 to 8 
characters.

min        =  4   = pass
max        =  8   = Pass
min-1      =  3   = fail
min+1      =  5   = pass
max-1      =  7   = pass
max+1      =  9   = fail