Haskell, 46 bytes

d :: Floating c => [c] -> [c] -> c d a=sqrt.sum.map((^2).uncurry(flip(-))).zip a 

Examples:

Prelude> d [1] [3] 2.0 Prelude> d [1,1] [1,1] 0.0 Prelude> d [1,2,3,4] [5,6,7,8] 8.0 Prelude> d [1.5,2,-5] [-3.45,-13,145] 150.82938208452623 Prelude> d [13.37,2,6,-7] [1.2,3.4,-5.6,7.89] 22.50202213135522