Conversion/alloying materials (CAMs) represent a potential alternative to graphite as a Li-ion anode active material, especially for high-power applications. So far, however, essentially all studies on CAMs have been dealing with nano-sized particles, leaving the question of how the performance (and the de-/lithiation mechanism in general) is affected by the particle size. Herein, we comparatively investigate four different samples of Zn$_{0.9}$Co$_{0.1}$O with a particle size ranging from about 30 nm to a few micrometers. The results show that electrodes made of larger particles are more susceptible to fading due to particle displacement and particle cracking. The results also show that the conversion-type reaction in particular is affected by an increasing particle size, becoming less reversible due to the formation of relatively large transition metal (TM) and alloying metal nanograins upon lithiation, thus hindering an efficient electron transport within the initial particle, while the alloying contribution remains essentially unaffected. The generality of these findings is confirmed by also investigating Sn$_{0.9}$Fe$_{0.1}$O$_2$ as a second CAM with a substantially greater contribution of the alloying reaction and employing Fe instead of Co as a TM dopant.