Agastache is also known as "big leaf MINT". It can be seen from this alias that the leaf of Agastache is bigger than that of mint.
In addition to comparing the size of the two leaves, you can also take a look at the base of the leaf, which is the part connected with the petiole. The leaf base of Agastache rugosa is "heart-shaped", and the gap of the heart is relatively shallow. The leaf base of peppermint is wedge-shaped, or nearly round, that is, there is no "heart" shaped small gap. What's more, the leaves of Agastache seem to shrink, while the leaves of peppermint are more even.
Although both agastache and Mentha are cymose and flowery, there are still obvious differences. The growing part of the flower of Agastache rugosa is at the "top" of the main stem or side branches, which is known as "top growth" in Botany, and the flowers of Agastache rugosa are very dense, in the shape of cylindrical spikes. And mint flowers grow at the junction of leaves and main stems, i.e. "axillary". In short, the flowers of Agastache are growing on the top of the head, while the lotus is growing under the armpit.
