So can we put in trait connection, since these two are female protagonists for two melodramatic anime series?
No, a tag shouldn't be used so lightly otherwise soon enough you'd be categorizing 2 shounen shows as having trait connection.
Besides, the "drama" about these shows are very much not melodrama in the plot itself, but how split the fandoms are. Both are very much "love it or hate it" kind of show with most people agreeing that neither stands up to the hype it was built up to be prior to broadcast.