Uzumaki actually seem to have retained their Ashura lineage for a longer period of time than the main Senju clan. The Senju vanished into obscurity shortly after forming Konoha, most likely merging their genes with other clans. The Uzumaki persisted until the destruction of the Whirlpool country decades later, retaining their powerful chakra and life force. There's a reason why Konoha relied on Kushina to host Kurama as Mito neared the end of her life, and why Madara needed to leave his Rinnegan to Nagato. The Uzumaki had, at that point, outlived the Senju clan, at least in terms of preserving their powerful genetic traits.
In the end, it's hard to separate the Senju from the Uzumaki; the main difference is that the Uzumaki have red hair and passed down powerful Sealing jutsu. The Senju at one point shared the same powerful life force, but lost this trait due to intermarriage.
