Buy Onitama if you want a two-player-only design and a two-minute rules explanation; Arcane Wonders lists 2 players, 15 minutes. Buy Santorini if you want variety from its god powers and a striking table presence; Roxley lists 2-4 players, 20 minutes.
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These are the two light abstracts we recommend to a pair who wants something with no luck but not much rules overhead. Both teach fast, both finish inside 20 minutes, and both are genuinely good.
The split is between a tight two-player-only design and a more flexible box with more variety in it.
02Where the variety comes from
Onitama gets its variety from the five move cards drawn from sixteen at setup. The rules never change; the tools do, and the passing mechanism -- using a card hands it to your opponent -- is constant.
Santorini gets its variety from god powers, which each break a rule outright. That is a bigger swing: a power can change what winning means, not just how you move. Some matchups are lopsided as a result.
Onitama's variety is tuned and Santorini's is wild. Which you prefer is mostly temperament, but a pair who wants a fair contest every time should take Onitama, and a pair who wants the box to surprise them should take Santorini.
03Table presence and age
Santorini wins on presence by a distance. It builds a three-dimensional island in chunky molded pieces, and that is genuinely persuasive to someone who does not think board games are for them. Onitama is a small mat and some pawns.
Santorini is also listed at ages 8+ against Onitama's 14+, which is a wide gap for two games of similar rules weight. If a younger player is ever going to join, that matters.