  We present models for the formation of terrestrial planets, and the
collisional evolution of debris disks, in planetary systems that contain
multiple unstable gas giants. We previously showed that the dynamics of the
giant planets introduces a correlation between the presence of terrestrial
planets and debris disks. Here we present new simulations that show that this
connection is qualitatively robust to changes in: the mass distribution of the
giant planets, the width and mass distribution of the outer planetesimal disk,
and the presence of gas in the disk. We discuss how variations in these
parameters affect the evolution. Systems with equal-mass giant planets undergo
the most violent instabilities, and these destroy both terrestrial planets and
the outer planetesimal disks that produce debris disks. In contrast, systems
with low-mass giant planets efficiently produce both terrestrial planets and
debris disks. A large fraction of systems with low-mass outermost giant planets
have stable gaps between these planets that are frequently populated by
planetesimals. Planetesimal belts between outer giant planets may affect debris
disk SEDs. If Earth-mass seeds are present in outer planetesimal disks, the
disks radially spread to colder temperatures. We argue that this may explain
the very low frequency of > 1 Gyr-old solar-type stars with observed 24 micron
excesses. Among the (limited) set of configurations explored, the best
candidates for hosting terrestrial planets at ~1 AU are stars older than 0.1-1
Gyr with bright debris disks at 70 micron but with no currently-known giant
planets. These systems combine evidence for rocky building blocks, with giant
planet properties least likely to undergo destructive dynamical evolution. We
predict an anti-correlation between debris disks and eccentric giant planets,
and a positive correlation between debris disks and terrestrial planets.
