Learn Russian: В отличие от турбины, новый глушитель не даёт больше мощности. - Unlike a turbine, a new muffler does not give more power.

It follows в отличие от (unlike / in contrast to). This is a compound preposition that always requires the Genitive case, which changes the feminine noun турбина to турбины.

Why is мощность (power) in the Genitive case (мощности) at the end of the sentence?

It follows the comparative word больше (more). Words expressing quantity or amount require the noun they quantify to be in the Genitive case. You can think of it as literally saying "more of power".

мощность is feminine, so why does its Genitive form end in -и instead of -ы?

Because мощность ends in a soft sign (-ь), making it a 3rd-declension feminine noun (like ночь or вещь). These nouns always take an -и ending in the Genitive, Dative, and Prepositional cases.

I see the verb is даёт. Why doesn't давать follow the standard pattern to become "давает"?