sameFringe[t1_, t2_] := TreeLeaves[t1] === TreeLeaves[t2];

t1 = Tree[{1, Tree[{2, Tree[{3, 4}]}]}];
t2 = Tree[{Tree[{1, 2}], Tree[{3, 4}]}];
t3 = Tree[{Tree[{1, 2}], Tree[{4, 3}]}];

TableForm[{Map[Tree[#, ImageSize -> Tiny] &, {t1, t2, t3}], Map[TreeData /@ TreeLeaves[#] &, {t1, t2, t3}]},
	  TableDepth -> 2, TableHeadings -> {{"Tree", "Leaves"}, {"t1", "t2", "t3"}}, TableAlignments -> Center]

{sameFringe[t1, t2], sameFringe[t1, t3]}