Context : Aims : We performed a detailed membership selection and studied the accretion properties of low-mass stars in the two apparently very similar young ( 1-10 Myr ) clusters \sigma Ori and \lambda Ori . Methods : We observed 98 and 49 low-mass ( 0.2 - 1.0 M _ { \sun } ) stars in \sigma Ori and \lambda Ori respectively , using the multi-object optical spectrograph FLAMES at the VLT , with the high-resolution ( R \sim 17,000 ) HR15N grating ( 6470 - 6790 Å ) . We used radial velocities , Li and H \alpha to establish cluster membership and H \alpha and other optical emission lines to analyze the accretion properties of members . Results : We identified 65 and 45 members of the \sigma Ori and \lambda Ori clusters , respectively and discovered 16 new candidate binary systems . We also measured rotational broadening for 20 stars and estimated the mass accretion rates in 25 stars of the \sigma Ori cluster , finding values between 10 ^ { -11 } and 10 ^ { -7.7 } M _ { \odot } yr ^ { -1 } and in 4 stars of the \lambda Ori cluster , finding values between 10 ^ { -11 } and 10 ^ { -10.1 } M _ { \odot } yr ^ { -1 } . Comparing our results with the infrared photometry obtained by the Spitzer satellite , we find that the fraction of stars with disks and the fraction of active disks is larger in the \sigma Ori cluster ( 52 \pm 9 % and 78 \pm 16 % ) than in \lambda Ori ( 28 \pm 8 % and 40 \pm 20 % ) . Conclusions : The different disk and accretion properties of the two clusters could be due either to the effect of the high-mass stars and the supernova explosion in the \lambda Ori cluster or to different ages of the cluster populations . Further observations are required to draw a definitive conclusion .