I can't tell you what characteristics the AE one has, sorry - but the Tropica Hygrophila 'compact' is a variation of Hygrophila corymbosa, growing much shorter internodes, therefore more compact in growth.
To be fair, I must tell you that such varieties sometimes go back to original. This will show by a single branch growing longer internodes (=look more "leggy") than standard Hygrophila 'compact'.
If this happens, just pinch off the "leggy" branch at base from original stem and the plant will again focus on the compact growth. If you leave the "leggy" branch, this will likely out-compete the original compact growth, by faster and more vigorous growth.
The same "problem" sometimes occur in Hygrophila polysperma 'rosanervig' and Lindernia 'variegata', going back to all green in some branches. Solution is again, to trim away the branch of unwanted, green growth, so plant can focus on the rosanervig/variegated branches.