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Magnetoelectric resonators have been studied for the detection of small amplitude and low frequency magnetic fields via the delta-E effect, mainly in fundamental bending or bulk resonance modes. Here, we present an experimental and theoretical investigation of magnetoelectric thin-film cantilevers that can be operated in bending modes (BMs) and torsion modes (TMs) as a magnetic field sensor. A magnetoelastic macrospin model is combined with an electromechanical finite element model and a general description of the delta-E effect of all stiffness tensor components <i>C_ij</i> is derived. Simulations confirm quantitatively that the delta-E effect of the <i>C</i>₆₆ component has the promising potential of significantly increasing the magnetic sensitivity and the maximum normalized frequency change <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>f</mi><mi mathvariant="normal">r</mi></msub></mrow></semantics></math></inline-formula>. However, the electrical excitation of TMs remains challenging and is found to significantly diminish the gain in sensitivity. Experiments reveal the dependency of the sensitivity and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>f</mi><mi mathvariant="normal">r</mi></msub></mrow></semantics></math></inline-formula> of TMs on the mode number, which differs fundamentally from BMs and is well explained by our model. Because the contribution of <i>C</i>₁₁ to the TMs increases with the mode number, the first-order TM yields the highest magnetic sensitivity. Overall, general insights are gained for the design of high-sensitivity delta-E effect sensors, as well as for frequency tunable devices based on the delta-E effect.