Will you be able/willing to remove the cabinets to refinish them OR do they stay in place during that process?
It looks like water damage at the base on the side. It will just return unless you make it totally waterproof. A molding would cover it and be replaceable.
Refinishing the entire cabinets will be a big job, but cheaper than buying new for sure.
If the sides are veneer over particle board, then it will be difficult to repair any damage.
Sanding will be almost out of the question if it's veneer. Only a finish restorer will work safely and even them it may lift the veneer unless it's glued down really well from the factory.
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