Total Recommendations: 5
Both feature a girl who's whisked away to another world. Fushigi Yugi has far more romance, with a lot of action, comedy, and drama, while Escaflowne has a fairly standard shounen plot with a dash of romance.
Usagi Drop and Tokyo Godfathers are both about people who are unexpectedly put in charge of a kid, and come to love that kid. Usagi Drop is less dramatic, but they both are very heartwarming.
Both deal with a girl who's learning to deal with their magical abilities, and at the same time try to figure out how to deal with their feelings for the guys they like.
Higurashi is a supernatural horror/ mystery show. Kara no Kyoukai is similar in that it is a series of 'movies' in non-sequentioal order, and you must peice together what was happening and when. It is a story of a girl who is given supernatural powers and eventually comes to work for a supernatural detective agency. She isn't quite sane, has no compunction about killing when it's needed, and is drawn into several happenings that are of the otherworldy variety. Blood and gore aren't the only things that make these series, a smart plot is, too! And that is what these shows have in spades.
Both feature sweet, caring females in the lead. They are laid-back, with occasional moments of sxcitement, but generally are relaxing (sorta) slice-of-life animes.