In this paper, we formulate two multi-objective optimization problems (MOOPs) in orthogonal frequency-division multiple access (OFDMA)-based in-band full-duplex (IBFD) wireless communications.~The aim of this study is to exploit the performance trade-off between uplink and downlink where a wireless radio simultaneously transmits and receives in the same frequency.~We consider maximizing the system throughput as the first MOOP and minimizing the system aggregate power consumption as the second MOOP between uplink and downlink,~while taking into account the impact of self-interference~(SI)~and quality of service provisioning.~We study the throughput and the transmit power trade-off between uplink and downlink via solving these two problems.~Each MOOP is a non-convex mixed integer non-linear programming~(MINLP)~which is generally intractable. In order to circumvent this difficulty, a penalty function is introduced to reformulate the problem into a mathematically tractable form.~Subsequently,~each MOOP is transformed into a single-objective optimization problem~(SOOP)~via the weighted Tchebycheff method which is addressed by majorization-minimization~(MM)~approach. Simulation results demonstrate an interesting trade-off between the considered competing objectives.