Fire Emblem: Awakening, is a marriage* of the Fire Emblem series. It took a little bit of everything from just about each game. The series was doomed to end if Awakening did not sell enough, so they tried to cram in the best of everything. For example, open world freedom and monster battles originated in Gaiden, and was later revisited in Sacred Stones.
Mechanically, Genealogy of the Holy War is all over Awakening. The marriage system is the first example, where the female characters had a designated child, and their stats/skills were to be influenced by that of the two parents. In addition, a number of elements that are standard in Fire Emblem first took foothold in Jugdral, such as skills, the weapon triangle, and honestly developed characters in general. Your units just felt more like people.
Actual literal elements of Jugdral are present in Awakening, which leaves one to wonder how truly connected the different worlds/continents of Fire Emblem are. The 12 Deadlords, and the sacred power they wield, originated in Genealogy of the Holy War. Many of these weapons would become series staples, hence why the names may be familiar. There's also just the part where much of it is inspired by Norse mythology, not unusual for a fantasy universe.
*Pun unintended.