#Pyth, 11 10 bytes

Thanks to @FryAmTheEggman for teaching me the power of ;!

qFmSr-d;0Q

Try it here!

Takes a list of two strings as input.

##Explanation

qFmSr-d;0Q    # Q = input

  m      Q    # map Q with d as lambda variable
     -d;      # filter spaces out of the string
    r   0     # convert to lowercase
   S          # sort all characters in string
qF            # Unfold resulting list and check for equality

Pyth, 11 10 bytes

Thanks to @FryAmTheEggman for teaching me the power of ;!

qFmSr-d;0Q

Try it here!

Takes a list of two strings as input.

Explanation

qFmSr-d;0Q    # Q = input

  m      Q    # map Q with d as lambda variable
     -d;      # filter spaces out of the string
    r   0     # convert to lowercase
   S          # sort all characters in string
qF            # Unfold resulting list and check for equality

#Pyth, 11 bytes

qFmSr-d\ 0Q

Try it here!

Takes a list of two strings as input.

##Explanation

qFmSr-d\ 0Q    # Q = input

  m       Q    # map Q with d as lambda variable
     -d\       # filter spaces out of the string
    r    0     # convert to lowercase
   S           # sort all characters in string
qF             # Unfold resulting list and check for equality

#Pyth, 11 10 bytes

Thanks to @FryAmTheEggman for teaching me the power of ;!

qFmSr-d;0Q

Try it here!

Takes a list of two strings as input.

##Explanation

qFmSr-d;0Q    # Q = input

  m      Q    # map Q with d as lambda variable
     -d;      # filter spaces out of the string
    r   0     # convert to lowercase
   S          # sort all characters in string
qF            # Unfold resulting list and check for equality

#Pyth, 12 bytes

qFmSr-d\ 0.z

Try it here!

#Pyth, 11 bytes

qFmSr-d\ 0Q

Try it here!

Takes a list of two strings as input.

##Explanation

qFmSr-d\ 0Q    # Q = input

  m       Q    # map Q with d as lambda variable
     -d\       # filter spaces out of the string
    r    0     # convert to lowercase
   S           # sort all characters in string
qF             # Unfold resulting list and check for equality