  We present a comparative study of spherically symmetric, localized,
particle-like solutions for spin $s=0,1/2$ and $1$ gravitating fields in a
$D$-dimensional, asymptotically flat spacetime. These fields are massive,
possessing a harmonic time dependence and no self-interaction. Special
attention is paid to the mathematical similarities and physical differences
between the bosonic and fermonic cases. We find that the generic pattern of
solutions is similar for any value of the spin $s$, depending only on the
dimensionality of spacetime, the cases $D=4,5$ being special.
