There are many questions which sound similar or the same for groups and Lie algebras. Some (very few, actually) of those questions have identical solutions and answers. Some have identical answers but very different solutions. Some have different answers and different solutions.

I am not talking about situations where one have a strictly defined (functorial) correspondence of some sort which allows to reduce almost automatically some questions from groups to Lie algebras, like Lie groups-Lie algebras, or Malcev(-like) correspondence.

For simplicity, let us confine to finite groups and finite-dimensional Lie algebras over a field. A few examples of what I have in mind:

Suppose a group (resp. Lie algebra) is represented as a (not necessarily direct) product (resp. sum) of two nilpotent subgroups (resp. subalgebras). Is it true that the group (resp. Lie algebra) is solvable?

Suppose a group (resp. Lie algebra) is commutative-transitive: $[x,y] = 1$ (resp. 0), $[y,z] = 1$ (resp. 0), and $y \ne 1$ (resp. 0) implies $[x,z] = 1$ (resp. 0). What can be said about its structural properties?

**(edit: added a couple of hours later)**(Lyndon-)Hochschild-Serre spectral sequence connecting group (resp. Lie algebra) (co)homology with (co)homology of its normal subgroup (resp. ideal) and the respective quotient.

As far as I know, both questions 1. and 2. have very similar answers for groups and Lie algebras, in some particular situations admit (almost) identical proofs or fragments of proofs, but in the whole generality the proofs are very different, with group-theoretic proof not utilizing in any way a Lie-algebraic one, and vice versa. As for 3., initially the group- and Lie-algebraic cases were given very similar, but disjoint proofs, and later were interpreted as particular instances of the Grothendieck (?) spectral sequence.

**Question.**
Is it possible, looking on a property of groups/Lie algebras expressed as a formula in the appropriate first- or second-order theory, to predict solely on syntaxical/logical ground, whether this property would convey similar or different results in respective categories? On the other hand, is there some (metamathematical, I dare to say) principle which would make this impossible?

I realize that the question is probably too vague, and I would appreciate any help in making it more precise and interesting.