In this study, we analysed about \(\sim \) 13 years of publicly available data from MAXI and Swift/BAT to examine the long-term source evolution of 42 transient low-mass X-ray binaries. The sample consists of 11 confirmed black hole X-ray binaries (BHXBs), 10 black hole candidates (BHC), and 21 neutron star X-ray binaries (NSXBs). Outbursts and flaring activities studied over 13 years show that 19/21 NSXBs spend significantly longer time in the hard state (observations for which hardness ratio is \(\ge \) 0.2) while 15/21 BHXB+XRC spend substantially longer time in the soft state (observations for which hardness ratio is < 0.2). The frequency distribution of the hardness ratio clearly shows two distinct distributions for BHXBs and NSXBs, with their peaks separated: NSXBs prefer harder values, while BHXBs prefer softer values of hardness. Our model-independent analysis for 42 transient sources shows that statistically NSXBs do not prefer to show a canonical high soft state as observed in BHXBs. Additionally, the probability distribution of the duration of the 2-20 keV X-ray outburst is observed to peak at a significantly longer duration (>100 days) for BHXBs than for NSXBs (15-60 days). Our analysis shows that among candidate sources, Swift J1728.9-3613, MAXI J1535-571, MAXI J1659-152, EXO 1846-031 show a ‘q’ diagram in the HID and prefer to align with the HID frequency distribution of BHXBs that show ‘q’ diagram, MAXI J1305-704 and MAXI J1836-194 align with frequency distribution of black hole sources without ‘q’ diagram while MAXI J1848-015 shows the HID distribution similar to NSXBs, indicating a neutron star accretor. Therefore, a long-term statistical study of MAXI and Swift/BAT X-ray outbursts from a large sample of transient sources may be used to distinguish BHXB from NSXB.
