  We compare the structure and substructure of dark matter halos in model
universes dominated by collisional, strongly self interacting dark matter
(SIDM) and collisionless, weakly interacting dark matter (CDM). While SIDM
virialised halos are more nearly spherical than CDM halos, they can be
rotationally flattened by as much as 20% in their inner regions. Substructure
halos suffer ram-pressure truncation and drag which are more rapid and severe
than their gravitational counterparts tidal stripping and dynamical friction.
Lensing constraints on the size of galactic halos in clusters are a factor of
two smaller than predicted by gravitational stripping, and the recent detection
of tidal streams of stars escaping from the satellite galaxy Carina suggests
that its tidal radius is close to its optical radius of a few hundred parsecs
--- an order of magnitude smaller than predicted by CDM models but consistent
with SIDM. The orbits of SIDM satellites suffer significant velocity bias
$\sigma_{SIDM}/\sigma_{CDM}=0.85$ and are more circular than CDM,
$\beta_{SIDM}} \approx 0.5$, in agreement with the inferred orbits of the
Galaxy's satellites. In the limit of a short mean free path, SIDM halos have
singular isothermal density profiles, thus in its simplest incarnation SIDM is
inconsistent with galactic rotation curves.
