In this paper, we analytically study the regime in which practical full-duplex systems can achieve larger rates than an equivalent half-duplex systems. The key challenge in practical full-duplex systems is uncancelled self-interference signal, which is caused by a combination of hardware and implementation imperfections. Thus, we first present a signal model which captures the effect of significant impairments such as oscillator phase noise, low-noise amplifier noise figure, mixer noise, and analog-to-digital converter quantization noise. Using the detailed signal model, we study the rate gain region, which is defined as the region of received signal-of-interest strength where full-duplex systems outperform half-duplex systems in terms of achievable rate. The rate gain region is derived as a piecewise linear approximation in log-domain, and numerical results show that the approximation closely matches the exact region. Our analysis shows that when phase noise dominates mixer and quantization noise, full-duplex systems can use either active analog cancellation or baseband digital cancellation to achieve near-identical rate gain regions. Finally, as a design example, we numerically investigate the full-duplex system performance and rate gain region in typical indoor environments for practical wireless applications.