Finding two-player games that still feel social rather than duel-like

My partner and I want more two-player games, but pure head-to-head duels turn our evenings into silent concentration contests. We like making decisions and teasing each other about them; we don't love attacking one another's progress. Cooperative games are one option, though we're interested in competitive scoring that still feels relaxed. Any recommendations that encourage table talk and interesting shared decisions without the constant ‘I destroy your thing’ dynamic?