The Will Rogers Phenomenon
Pyth, 29 28 26 24 bytes
Thanks to @Jakube for saving me 3 bytes with .p and L.
Very simple, checks if any elements in list 2 are greater than mean of list 1 and less than mean of list 2, then repeats with list 1 and list 2 switched.
Lcsblbff&amp;&gt;YyhT&lt;YyeTeT.pQ

Prints an a non-empty list for truthy, and [] for falsey.
L                    Define y(b). Pyth has no builtin for mean
 c                   Float div
  sb                 Sum of b
  lb                 Length of b
f        .pQ         Filter all permutations of input
 f     eT            Filter the last element of the filter var
  &amp;                  Logical and
   &gt;Y                Inner filter var greater than
    y                Call the mean function we defined earlier
     hT              First element of outer filter var
   &lt;Y                Inner filter var less than
    y                Mean of
     eT              Last element of outer filternvar

Try it online here.
Test Suite.