Orthogonal time frequency space (OTFS) modulation, a delay-Doppler (DD) domain communication scheme exhibiting strong robustness against the Doppler shifts, has the potentials to be employed in LEO satellite communications. However, the performance comparison with the orthogonal frequency division multiplexing (OFDM) modulation and the resource allocation scheme for multiuser OTFS-based LEO satellite communication system have rarely been investigated. In this paper, we conduct a performance comparison under various channel conditions between the OTFS and OFDM modulations, encompassing evaluations of sum-rate and bit error ratio (BER). Additionally, we investigate the joint optimal allocation of power and delay-Doppler resource blocks aiming at maximizing sum-rate for multiuser downlink OTFS-based LEO satellite communication systems. Unlike the conventional modulations relaying on complex input-output relations within the Time-Frequency (TF) domain, the OTFS modulation exploits both time and frequency diversities, i.e., delay and Doppler shifts remain constant during a OTFS frame, which facilitates a DD domain input-output simple relation for our investigation. We transform the resulting non-convex and combinatorial optimization problem into an equivalent difference of convex problem by decoupling the conditional constraints, and solve the transformed problem via penalty convex-concave procedure algorithm. Simulation results demonstrate that the OTFS modulation is robust to carrier frequency offsets (CFO) caused by high-mobility of LEO satellites, and has superior performance to the OFDM modulation. Moreover, numerical results indicate that our proposed resource allocation scheme has higher sum-rate than existed schemes for the OTFS modulation, such as delay divided multiple access and Doppler divided multiple access, especially in the high signal-to-noise ratio (SNR) regime.