Connection between algebraic logic and computational complexity of logics?
The example you gave extends as follows:


SAT for arbitrary lattices (meaning, is a given formula satisfiable in some lattice) is polynomial-time decidable
SAT for modular lattices is Turing undecidable:
Freese, Ralph, Free modular lattices, Trans. Am. Math. Soc. 261, 81-91 (1980). ZBL0437.06006.
SAT for Boolean algebras is NP-complete


So while modular lattices are in between Boolean algebras and arbitrary lattices, they are the most complicated.