Rivka told Yaakov to run away from Eisav because "Lama Eshkol Gam Shnaichem Yom Echad", why should I lose two children in one day. Rashi explains that if Eisav kills Yaakov his children will kill Eisav right away. This Rashi says was nevuah that came out of her mouth since they both died in one day. The gemara in Sotah 13 says that although they did not die the same day Eisav was killed by Chushim ben Dan the day Yaakov was buried. However asks Rav Shimshon Pincus, since the fact remains that they did not die the same day so what kind of nevuah was this?
He answers that the gemara says in Taanis 5 that "Yaakov Avinu Lo Meis", Yaakov Avinu never died (the meaning of this is not within my scope to explain).
Therefore the day of Yaakov's death was not the day he was taken from us. Although (whatever it means) he was still alive when they placed him the Meoras HaMachpela, it was the day he was taken away from us.
Therefore it turns out that indeed Yaakov and Eisav were taken the same day.