We can do some algebraic simplification, using the law
if P  then True else Q  is same as P || Q :

(<||>) m1 m2 = do
   r1 <- m1
   r2 <- m2
   return (r1 || r2)

Which reminds me of the definition of liftM2
(from Control.Monad):

liftM2 f m1 m2          = do { x1 <- m1; x2 <- m2; return (f x1 x2) } 

 And so we can golf down to:
(<||>) = liftM2 (||)

Now, instead of using liftM2 from Control.Monad, I could as well use liftA2 from Control.Applicative :

(<||>) = liftA2 (||)

So my questions to the experts:

1> Are these equivalent or am I missing something?
2> Any thumb rules on when to use Control.Monad and when to use Control.Applicative?

Rusi