#Pyth, 57 55 53 bytes

AQjd[G"is"@c"equal to
greater than
less than"b._-GHH)

This basically does:

["less than", "greater than", "equal to"][sign_of(A-B)]

Saved 2 bytes thanks to @AlexA.'s suggestion of using A instead of J and K and another 2 bytes by replacing the whole addition mess with a simpler subtraction.

Live demo and test cases.

##55-byte version

AQjd[G"is"@c"less than
greater than
equal to"b+gGHqGHH)

Live demo and test cases.

##57-byte version:

jd[JhQ"is"@c"less than
greater than
equal to"b+gJKeQqJKK)

Live demo and test cases.

Pyth, 57 55 53 bytes

AQjd[G"is"@c"equal to
greater than
less than"b._-GHH)

This basically does:

["less than", "greater than", "equal to"][sign_of(A-B)]

Saved 2 bytes thanks to @AlexA.'s suggestion of using A instead of J and K and another 2 bytes by replacing the whole addition mess with a simpler subtraction.

Live demo and test cases.

55-byte version

AQjd[G"is"@c"less than
greater than
equal to"b+gGHqGHH)

Live demo and test cases.

57-byte version:

jd[JhQ"is"@c"less than
greater than
equal to"b+gJKeQqJKK)

Live demo and test cases.

#Pyth, 57 55 bytes

AQjd[G"is"@c"less than
greater than
equal to"b+gGHqGHH)

This basically does:

["less than", "greater than", "equal to"][(A>=B)+(A==B)]

Saved 2 bytes thanks to @AlexA.'s suggestion of using A instead of J and K.

Live demo and test cases.

##57-byte version:

jd[JhQ"is"@c"less than
greater than
equal to"b+gJKeQqJKK)

Live demo and test cases.

#Pyth, 57 55 53 bytes

AQjd[G"is"@c"equal to
greater than
less than"b._-GHH)

This basically does:

["less than", "greater than", "equal to"][sign_of(A-B)]

Saved 2 bytes thanks to @AlexA.'s suggestion of using A instead of J and K and another 2 bytes by replacing the whole addition mess with a simpler subtraction.

Live demo and test cases.

##55-byte version

AQjd[G"is"@c"less than
greater than
equal to"b+gGHqGHH)

Live demo and test cases.

##57-byte version:

jd[JhQ"is"@c"less than
greater than
equal to"b+gJKeQqJKK)

Live demo and test cases.

#Pyth, 57 bytes

jd[JhQ"is"@c"less than
greater than
equal to"b+gJKeQqJKK)

This basically does:

["less than", "greater than", "equal to"][(A>=B)+(A==B)]

Live demo and test cases.

#Pyth, 57 55 bytes

AQjd[G"is"@c"less than
greater than
equal to"b+gGHqGHH)

This basically does:

["less than", "greater than", "equal to"][(A>=B)+(A==B)]

Saved 2 bytes thanks to @AlexA.'s suggestion of using A instead of J and K.

Live demo and test cases.

##57-byte version:

jd[JhQ"is"@c"less than
greater than
equal to"b+gJKeQqJKK)

Live demo and test cases.