Wasserstein distances define a metric between probability measures on arbitrary metric spaces, including meta-measures (measures over measures). The resulting Wasserstein over Wasserstein (WoW) distance is a powerful, but computationally costly tool for comparing datasets or distributions over images and shapes. To lower the computational burden, we propose to leverage the isometry between the 1d Wasserstein space and the quantile functions. For this purpose, we introduce a general sliced Wasserstein framework for arbitrary Banach spaces. Due to the 1d Wasserstein isometry, this framework defines a sliced distance between 1d meta-measures via infinite-dimensional projections, parametrized by Gaussian processes. Combining this 1d construction with a second slicing of the underlying domain yields the double-sliced Wasserstein (DSW) metric for general meta-measures. Numerical experiments on datasets, shapes, and images validate DSW as a scalable substitute for the WoW distance. Moreover, our functional framework can be used to introduce a novel slicing of the Gromov-Wasserstein (GW) distance, which allows to compare shapes and heterogeneous data. Former GW slicings are restricted to the Euclidean geometry and lose the desired invariance to isometries, strongly limiting their application in practice. Our novel sliced GW lower bound significantly reduces the numerical effort while remaining invariant to isometric transformations and allowing the comparison of arbitrary geometries.