  Two fundamental invariants attached to a projective variety are its classical
algebraic degree and its Euclidean Distance degree (ED degree). In this paper,
we study the asymptotic behavior of these two degrees of some Segre products
and their dual varieties. We analyze the asymptotics of degrees of
(hypercubical) hyperdeterminants, the dual hypersurfaces to Segre varieties. We
offer an alternative viewpoint on the stabilization of the ED degree of some
Segre varieties. Although this phenomenon was incidentally known from
Friedland-Ottaviani's formula expressing the number of singular vector tuples
of a general tensor, our approach provides a geometric explanation. Finally, we
establish the stabilization of the degree of the dual variety of a Segre
product $X\times Q_{n}$, where $X$ is a projective variety and $Q_n\subset
\mathbb{P}^{n+1}$ is a smooth quadric hypersurface.
