If you would like your solution to generalise to more than two matrices as well, something like this could work:

MapThread[List /* MaximalBy[Last] /* First, {A, B}]

/* there is the RightComposition function.

Very good, Chaib, thank you for your answer!

There may be other commands or ways to do this, but with the "If", "Table" and "Part" commands you can also do this:

A = {{1, 2, 3}, {5, 6, 7}, {5, 7, 9}, {3, 3, 8}};
B = {{2.3, 2.8, 2.5}, {3, 4, 10}, {4, 2, 3}, {9, 6.3, 3}};

A // MatrixForm
B // MatrixForm

AB = Table[
   If[Last@A[[i]] > Last@B[[i]], A[[i]], B[[i]]], {i, 1, Length@A}];

AB // MatrixForm

If the last terms are the same and you want the row to come from A, change to >= , because with only > and the last terms are the same, the row will come from B.