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APL (Dyalog Unicode), 18 bytes

(⍋-⍒)∘↑(⍎¨∊∘⎕D⊆⊢)¨

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Takes the input as an array of strings as the right argument. Outputs ¯1 1, 0 0, 1 ¯1 for <, =, > respectively.

(⍎¨∊∘⎕D⊆⊢)¨ on each input

  • ∊∘⎕D⊆⊢ group all occurrences of digits, that is, split on .

  • ⍎¨ and convert each of these occurrences to a number

convert to a matrix, where the first input is on the top row and the second one in the bottom, padding with 0s where necessary

(⍋-⍒)∘ and

  • - subtract
    • the indices of the rows sorted in descending order
    • from the indices of the rows sorted in ascending order