The application of surface acoustic wave (SAW) devices for the measurement of magnetic fields has found a growing interest in recent years due to their ability to detect fields even in the lower pT range. As the sensitive element in these devices amorphous magnetostrictive thin films such as the alloy FeCoSiB seem to be particularly promising due to their high magnetostriction with simultaneously having a low magnetic anisotropy. However, the applicability of FeCoSiB to different piezoelectric SAW substrate materials and the influence on the magnetic properties and sensitivity has not been studied so far. Thus, three different substrate materials namely quartz, lithium niobate (LiNbO3) and langasite (La3Ga5SiO14) exhibiting shear horizontal SAWs are presented in this work. This so-called love waves result from a piezoelectric substrate generating shear horizontal waves capped with a guiding layer confining the acoustic wave at the surface. Operating in a delay line configuration the magnetoelastically-induced change of shear modulus of the sensitive layer yields in a corresponding phase shift of the acoustic wave. The quartz based SAW devices with a working frequency of approximately 150 MHz show a passband of 4 MHz and a limit of detection (LOD) of 120 pT/√Hz at 10 Hz. Lithium niobate having a six times higher electromechanical coupling coefficient and langasite providing a lower magnetic anisotropy of the FeCoSiB layer both have the potential for even higher sensitivities.