We study the stellar population properties of 182 spectroscopically confirmed (MUSE/VLT) Lyα emitters (LAEs) and 450 photometrically selected Lyman-break galaxies (LBGs) at z = 2.8–6.7 in the Hubble Extreme Deep Field. Leveraging the combined power of Hubble Space Telescope and JWST NIRCam and MIRI observations, we analyze their rest-frame UV-through-near-IR spectral energy distributions, with MIRI playing a crucial role in robustly assessing the LAEs' stellar masses and ages. Our LAEs are low-mass objects (log₁₀(M_⋆/M_⊙)≃7.5) with little or no dust extinction (E(B − V) ≃ 0.1) and a blue UV continuum slope (β ≃ −2.2). While 75% of our LAEs are young (<100 Myr), the remaining 25% have significantly older stellar populations (≥100 Myr). These old LAEs are statistically more massive, less extinct, and have lower specific star formation rate than young LAEs. Besides, they populate the plane of M_⋆ versus star formation rate along the main sequence of star-forming galaxies, while young LAEs populate the starburst region. The comparison between the LAEs' properties and those of a stellar-mass-matched sample of LBGs shows no statistical difference between these objects, except for the LBGs' redder UV continuum slope and marginally larger E(B − V) values. Interestingly, 48% of the LBGs have ages <10 Myr and are classified as starbursts, but lack detectable Lyα emission. This is likely due to H i resonant scattering and/or dust-selective extinction. Overall, we find that JWST observations are crucial in determining the properties of LAEs and shedding light on their comparison with LBGs.