Hi,
  

Both testings are necessary to test a application.

Both Testing's are important because, 

Equivalence partitioning is useful for picking a sample from
group or partion .

Boundary value analysis is useful for checking boundary
values ,because most of them commit mistakes at boundaries
(< , <= ,> ,>=)

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

Both Testing's are important it depends on the situation 
what testing should be done and when should be done. 

equivalenc partitioning is used to define a type of input 
test data and it is done to reduse the number of test 
cases . 
example if only character data is to be used then 

          valid            invalid
          A to Z           Special symbol 
          a to z           Blank spaces.
          0 to 9

            
Boundary value analysis is used to define a size of input 
test data to reduse memory crash chances. to check loops in 
programm.
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