This work aimed to assess the biomechanics, using the finite element method (FEM), of traditional titanium Morse taper (MT) dental implants compared to one-piece implants composed of zirconia, polyetheretherketone (PEEK), carbon fiber-reinforced PEEK (CFR-PEEK), or glass fiber-reinforced PEEK (GFR-PEEK). MT and one-piece dental implants were modeled within a mandibular bone section and loaded on an oblique force using FEM. A MT implant system involving a Ti6Al4V abutment and a cp-Ti grade IV implant was compared to one-piece implants composed of cp-Ti grade IV, zirconia (3Y-TZP), PEEK, CFR-PEEK, or GFR-PEEK. Stress on bone and implants was computed and analyzed while bone remodeling prediction was evaluated considering equivalent strain. In comparison to one-piece implants, the traditional MT implant revealed higher stress peak (112 MPa). The maximum stresses on the one-piece implants reached ~80 MPa, regardless their chemical composition. MT implant induced lower bone stimulus, although excessive bone strain was recorded for PEEK implants. Balanced strain levels were noticed for reinforced PEEK implants of which CFR-PEEK one-piece implants showed proper biomechanical behavior. Balanced strain levels might induce bone remodeling at the peri-implant region while maintaining low risks of mechanical failures. However, the strength of the PEEK-based composite materials is still low for long-term clinical performance.