Superparamagnetic relaxometry (SPMR) is a new technology used for detection and localization of cells tagged with super-paramagnetic nanoparticles. SPMR is one of the most promising methods for early cancer diagnosis with the potential for submillimeter size tumor resolution. SQUID-based gradiometers are very suitable for such sensitive measurements. Presently, most commonly used SPMR instruments consist of axial wire-wound gradiometers connected to SQUID-sensors placed inside tight superconducting shields. This configuration avoids flux trapping by the Josephson junctions during magnetization. A thin-film planar gradiometer integrated with a SQUID on a single chip traps flux, if it picks up even small portion of a magnetizing field. Thermal cycling is very slow, therefore it is not practical. Special measures must be applied such as newly developed methods of SQUIDs ac de-fluxing. Planar thin-film gradiometers have advantages over axial wire-wound gradiometers because of their much higher balance level, higher reliability, and reproducibility in production, and significant simplification of multichannel systems design. In this paper, we compare experimental results received using axial wire-wound and planar thin-film gradiometers. This comparison is based on SPMR measurements conducted using the seven-channel axial second-order gradiometer system and two systems with different geometries of the thin-film first-order planar gradiometer arrays. We discuss advantages and drawbacks of the two types of gradiometers.