Polycrystalline Sr2FeMoO6 (SFMO) samples with various grain sizes and densities of Fe∕Mo disorder defects were synthesized from sol-gel-derived precursors by means of a sample-encapsulation technique. The samples with perfect Fe∕Mo ordering exhibited metallic transport behavior and a large magnetoresistance (MR) effect, whereas the samples with a high-disorder density and small grain size showed a metal-insulator transition and lower MR values. It is suggested that a competition between intragranular and intergranular tunneling MR effects exists in the SFMO system. To confirm this competition, homocomposite samples consisting of two or three single-phase SFMO components with different grain sizes were designed. Large enhancement in low-field magnetoresistance (LFMR) was observed in the homocomposites, which could be attributed to the enhanced intergranular effect. It is thus concluded that the intergranular effect is more important to the LFMR than the intragranular effect.