Superconducting nanowire single-photon detectors (SNSPDs) have become a mainstream photon-counting technology that has been widely applied in various scenarios. So far, most multi-channel SNSPD systems, either reported in literature or commercially available, are polarization sensitive, that is, the system detection efficiency (SDE) of each channel is dependent on the state of polarization of the to-be-detected photons. Here, we reported an eight-channel system with fractal SNSPDs working in the wavelength range of 930 to 940 nm, which are all featured with low polarization sensitivity. In a close-cycled Gifford-McMahon cryocooler system with the base temperature of 2.2 K, we installed and compared the performance of two types of devices: (1) SNSPD, composed of a single, continuous nanowire and (2) superconducting nanowire avalanche photodetector (SNAP), composed of 16 cascaded units of two nanowires electrically connected in parallel. The highest SDE among the eight channels reaches 96−5+4%, with the polarization sensitivity of 1.02 and a dark-count rate of 13 counts per second. The average SDE for eight channels for all states of polarization is estimated to be 90 ± 5%. It is concluded that both the SNSPDs and the SNAPs can reach saturated, high SDE at the wavelength of interest, and the SNSPDs show lower dark-count (false-count) rates, whereas the SNAPs show better properties in the time domain. With the adoption of this system, we showcased the measurements of the second-order photon-correlation functions of light emission from a single-photon source based on a semiconductor quantum dot and from a pulsed laser. It is believed that this work will provide new choices of systems with single-photon detectors combining the merits of high SDE, low polarization sensitivity, and low noise that can be tailored for different applications.