Your theory may be correct. It could also be due to different seasonal soil moisture levels in the two locations, different amounts of sunlight, differences in the tree's before you purhcased them. Maybe one had a root going around in the container that is now causing the plant problems. Dig a few inches deep around the trunk and look for a root encircling the trunk tightly and buried into the swelling trunk. If you find it consult an arborist for the best way to handle the particular situation it is in.
Otherwise try watering and fertilizing the smaller plant more. Use turf fertilizer and apply a cup or two per inch of trunk diameter through a large area around the tree in spring, early summer and mid summer.
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