We report on Rossi X-Ray Timing Explorer observations of four type I X-ray bursters, namely, 1E 1724-3045, GS 1826-238, SLX 1735-269, and KS 1731-260. The first three were in a low state, with 1-200 keV X-ray luminosities in the range ~0.05-0.1LEdd (LEdd: Eddington luminosity for a neutron star, LEdd = 2.5 × 1038 ergs s-1), whereas KS 1731-260 was in a high state, with luminosity ~0.35LEdd. The low-state sources have very similar power spectra, displaying high-frequency noise up to ~200 Hz. For KS 1731-260, its power spectrum is dominated by noise at frequencies ≲20 Hz; in addition a quasi-periodic oscillation at 1200 Hz is detected in a segment of the observation. The 1-200 keV spectra of the low-state sources are all consistent with resulting from thermal Comptonization with an electron temperature (kTe) around 25-30 keV. For KS 1731-260, the spectrum is also dominated by thermal Comptonization, but with a much lower kTe ~ 3 keV and no significant hard X-ray emission. With the exception of GS 1826-238, they each have an underlying soft component, carrying at most ~25% of the total 1-200 keV luminosity. For all sources, we have detected an iron Kα line at 6.4 keV (although it is weak and marginal in 1E 1724-3045). A reflection component is present in the spectra of GS 1826-238 and SLX 1735-269, and for both we find that the reflecting medium subtends only a small solid angle (Ω/2π ~ 0.15, 0.28). The origin of the line and the reflection component is most likely to be irradiation of the accretion disk by the X-ray source. We suggest a model in which the region of main energy release, where hard X-rays are produced, would be an optically thin boundary layer merged with an advection-dominated accretion flow (ADAF) and would be responsible for the rapid variability observed. The soft component observed probably represents the unscattered emission from an optically thick accretion disk of variable inner radius. When the accretion rate increases, the inner disk radius shrinks and the strength of the reflected component and associated iron line increase. At the same time, the Comptonization region cools off in response to an increased cooling flux from the accretion disk and from the reprocessed/reflected component, thus leading progressively to a quenching of the hard X-ray emission. If low-state neutron stars (NSs) accrete via ADAFs, the observation of X-ray bursts, indicating that all the accreting matter actually accumulates onto the NS surface, argues against the existence of strong winds from such accretion flows. Finally, we discuss two criteria recently proposed to distinguish between nonquiescent black holes (BHs) and NSs that are not contradicted by existing observations. The first one states that, when thermal Comptonization is responsible for the hard X-ray emission, only BHs have kTe larger than ~50 keV. However, this criterion is weakened by the fact that there are NSs displaying nonattenuated power laws extending up to at least 200 keV, possibly implying nonthermal Comptonization or thermal Comptonization with kTe larger than 50 keV. The second criterion stipulates that only BHs are capable of emitting hard X-ray tails with 20-200 keV luminosities ≳1.5 × 1037 ergs s-1.