The importance of amorphous and nanocrystalline Fe-based soft magnetic materials is increasing annually. Thus, characterisation of the chemical compositions, alloying additives, and crystal structures is significant for obtaining the appropriate functional properties. The purpose of this work is to present comparative studies on the influence of Nb (1, 2, 3 at.%) and Mo (1, 2, 3 at.%) in Fe substitution on the thermal stability, crystal structure, and magnetic properties of a rapidly quenched Fe79.4Co5Cu0.6B15 alloy. Additional heat treatments in a vacuum (260–640 °C) were performed for all samples based on the crystallisation kinetics. Substantial improvement in thermal stability was achieved with increasing Nb substitution, while this effect was less noticeable for Mo-containing alloys. The heat treatment optimisation process showed that the least lossy states (with a minimum value of coercivity below 10 A/m and high saturation induction up to 1.7 T) were the intermediate state of the relaxed amorphous state and the nanocomposite state of nanocrystals immersed in the amorphous matrix obtained by annealing in the temperature range of 340–360 °C for 20 min. Only for the alloy with the highest thermal stability (Nb = 3%), the α-Fe(Co) nanograin grows, without the co-participation of the hard magnetic Fe3B, in a relatively wide range of annealing temperatures up to 460 °C, where the second local minimum in coercivity and core power losses exists. For the remaining annealed alloys, due to lower thermal stability than the Nb = 3% alloy, the Fe3B phase starts to crystallise at lower annealing temperatures, making an essential contribution to magneto-crystalline anisotropy, thus the substantial increase in coercivity and induction saturation. The air-annealing process tested on the studied alloys for optimal annealing conditions has potential use for this type of material. Additionally, optimally annealed Mo-containing alloys are less lossy materials than Nb-containing alloys in a frequency range up to 400 kHz and magnetic induction up to 0.8 T.