For s>−1, s∉N₀, we compare two natural types of fractional Laplacians (−Δ)^s, namely, the restricted Dirichlet and the spectral Neumann ones. We show that the quadratic form of their difference taken on the space H˜^s(Ω) is positive or negative depending on whether the integer part of s is even or odd. For s∈(0,1) and convex domains we prove also that the difference of these operators is positivity preserving on H˜^s(Ω). This paper complements (Musina and Nazarov, 2014; 2016) where similar statements were proved for the spectral Dirichlet and the restricted Dirichlet fractional Laplacians.