Due to their intrinsic low mechanical vibration level both, Joule-Thomson refrigerator and Pulse-Tube refrigerator are promising candidates for low noise cooling of high-Tc SQUIDs. We report here on a test comparing the performance of a commercial Joule-Thomson cooler and a single stage Pulse-Tube cooler used to operate one and the same HT rf SQUID under comparable conditions in shielded environment. In order to reduce vibrations the cold stages of both cooler systems were connected by flexible plastic lines of several meters length with their compressors. Operated in a liquid nitrogen cryostat, the white field noise of the SQUID was 40jT,/&z at frequencies above 30 Hz. A slightly higher white noise (about 6OfT/&z) was observed for operation with either of the two coolers. This is probably due to the vicinity of superinsulation to the SQUID. The Joule-Thomson cooler produced a somewhat higher low frequency excess noise below 30 Hz and some characteristic noise bands at intermediate frequencies (ca. 100 Hz -500 Hz). The Pulse-Tube cooler led to a spectrum of lines at multiples of the pulse frequency (4.6 Hz). Both effects could be attributed (using cross correlation measurements) to residual mechanical vibrations of the cold heads of both coolers.