We report scanning tunneling spectroscopic (STS) studies of the low-energy quasiparticle excitations of cuprate superconductors as a function of magnetic field and doping level. Our studies suggest that the origin of the pseudogap (PG) is associated with competing orders (COs), and that the occurrence (absence) of PG above the superconducting (SC) transition T c is associated with a CO energy CO larger (smaller) than the SC gap SC . Moreover, the spatial homogeneity of SC and CO depends on the type of disorder in different cuprates: For optimally and under-doped YBa 2 Cu 3 O 7 (Y-123), we find that SC < CO and that both SC and CO exhibit long-range spatial homogeneity, in contrast to the highly inhomogeneous STS in Bi 2 Sr 2 CaCu 2 O 8+x (Bi-2212). We attribute this contrast to the stoichiometric cations and ordered apical oxygen in Y-123, which differs from the non-stoichiometric Bi-to-Sr ratio in Bi-2212 with disordered Sr and apical oxygen in the SrO planes. For Ca-doped Y-123, the substitution of Y by Ca contributes to excess holes and disorder in the CuO 2 planes, giving rise to increasing inhomogeneity, decreasing SC and CO , and a suppressed vortex-solid phase. For electron-type cuprate Sr 0.9 La 0.1 CuO 2 (La-112), the homogeneous SC and CO distributions may be attributed to stoichiometric cations and the absence of apical oxygen, with CO < SC revealed only inside the vortex cores. Finally, the vortex core radius ( halo ) in electron-type cuprates is comparable to the SC coherence length SC , whereas halo ~ 10 SC in hole-type cuprates, suggesting that halo may be correlated with the CO strength.The vortex-state irreversibility line in the magnetic field versus temperature phase diagram also reveals doping dependence, indicating the relevance of competing orders to vortex pinning.