I'd do both. B. thunbergii will grow from seed, all the species will, but the fancy hybrids and cultivars won't come true,
Sow the berries when they're ripe in gritty, well drained compost, leave them outside to experience the winter weather. They'll germinate in spring.
I never open berries or shell nuts when I sow them Mr J. Stuff germinates naturally without all that.