The transverse emittance of the muon beam produced at the Neutrino Factory front-end needs to be decreased using ionisation cooling. The current baseline cooling lattice for the Neutrino Factory, FSIIA, achieves acceptable muon transmission and transverse emittance reduction. However, recent studies indicate that high magnetic field at the position of the RF cavities may limit their maximum achievable gradient, and, since the magnetic field at the RF position of FSIIA is large, the feasibility of this lattice has come under question. A new lattice, Bucked Coils, was designed obtaining four times lower magnetic field than FSIIA while also achieving comparable transmission within 30 mm of transverse acceptance. A detailed comparison between the two lattices is presented with respect to the beam dynamics and the magnetic field.