We present a compared analysis of some properties of 3-Sasakian and
3-cosymplectic manifolds. We construct a canonical connection on an almost
3-contact metric manifold which generalises the Tanaka-Webster connection of a
contact metric manifold and we use this connection to show that a 3-Sasakian
manifold does not admit any Darboux-like coordinate system. Moreover, we prove
that any 3-cosymplectic manifold is Ricci-flat and admits a Darboux coordinate
system if and only it is flat.