Spine works at all resolutions. The larger monitor will give you more space and would work great. Also, there is an Interface scale setting that can scale the UI up (or down). When scaled up, Spine uses source graphics that are twice as large, so they still look great. For example (click for full resolution):

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Please note Spine is currently limited to a single application window. In the future we'll support detaching views to move them to another window, but for now you'll have to use a single monitor or stretch the Spine window so it spans multiple monitors.