This isn't quite right. Just having different sized batteries connected will not cause one to drain the other. Now if one of those batteries is really old/weak, regardless of size, it may bring the resting voltage of the newer/stronger battery down to its level. Also, having mixed chemistry batteries connected can have a similar effect. Meaning, if you had a flooded lead battery and an agm battery connected it wouldn't be ideal. I've personally done that one for a short period of time(less than a year) and noticed no major ill effects, though the agm would rest at the same lower voltage of the flooded battery when connected. After disconnecting the two, the agm bounced back to where it was before.
Keep power and ground runs to the amps short as possible and make sure both connections are solid.