  Using as a testbed the recently proposed "gravcat" experimental scheme in
[1], we compare the properties of gravitational cat states in three
descriptions: (1) canonical quantum theory (CQT) combined with the Newtonian
limit of GR, (2) objective collapse theories (OCTs) extended to the regime of
semiclassical Newtonian gravity, and (3) OCTs extended to incorporate quantized
Newtonian gravity. For the CQT approach, we follow the treatment of Hu and
Anastopoulos in [2]. For the OCTs, we consider the GRW, CSL, DP, and Karolyhazy
theories, based on the semiclassical approaches of Derakhshani [3] and
Tilloy-Diosi [4], respectively, and we consider the most straightforward
extension of the aforementioned OCTs to the regime of quantized Newtonian
gravity. We show that the gravitational cat scheme can, in principle,
experimentally discriminate the quantum jumps in gravitational cat states
predicted by the CQT approach and the quantized-gravity OCTs (which we show
make effectively the same predictions as each other), from the predictions of
the semiclassical-gravitational OCTs. We also show that the GRW and Karolyhazy
versions of semiclassical gravity (based on Derakhshani's approach) make
distinctly different predictions from the CSL and DP versions of semiclassical
gravity (based either on Derakhshani's approach or the Tilloy-Diosi approach).
