The planets of the East and the West were once connected by the Ama-no-Hashidate. The culture that built it was destroyed countless years ago, and the two planets have had separate histories ever since. On the Western planet, ancient culture is experiencing a renaissance after a long period of war. Jeanne Kaguya D'Arc, a girl from the Western Planet, was prophesied to be the Savior of the World at her birth. With Leonard Da Vinci, she lands on the Eastern Planet, where Nobunaga "the Fool" longs for the power to change the world, as his planet is still locked in a war where many heroes vie for supremacy. When these two people meet, the culture of both worlds will be transformed.
Source: ANN. Will be replaced by a unique synopsis written by Anime-Planet and updated tags.
Hitomi was just a normal high school girl, until she was taken by the mysterious Van Fanel and dropped into a world of romance, magic and giant sword-wielding armor suits! Now Van, pilot of the famed armor suit Escaflowne; and Hitomi, whose hobby of predicting the future just became a frightening reality, must work together and fight the advanced technology of Zaibach: a force who want to shape Gaea to their visions of "peace". Follow Hitomi in her struggles against both these forces who seek to conquer this world, and her own confused heart.
Both Nobunaga the Fool and The Vision of Escaflowne feature civilizations on two adjacent worlds, a willingness to play fast and loose with real-world historical figures, tarot themes, a female character with latent ESP who is transported into a war-torn feudal situation and enables a lone prince traveling with an animalistic sidekick to pilot a unique mecha which confirms his kingship.
(This is based on seeing only the first episode of Nobunaga)
The time is centuries ago, during the Sengoku period; the place is feudal Japan. Political ambitions and bloodshed run rampant as rival warlords battle it out in an attempt to rule the nation. Some seek to spread their noble ideals, some seek to protect justice and yet others seek destruction. Date Masamune, Sanada Yukimumra and a variety of other warriors will fight it out time and time again; their actions helping to ultimately decide the fight of Japan.
Both of these series focus around the legendary Oda Nobunaga, and take place in a fictional feudal Japan. Both series have a ton of characters based on historical figures, and are loosely based off the wars during the Sengoku peroid in Japan. Both are action-packed, with bits of comedy thrown in. The major difference is Nobunaga the Fool has Sci-Fi elements thrown in. If you enjoyed one, I'm fairly certain you'd enjoy the other as well.