Learn Italian: Se studi la sua strategia, reagisci meglio di lui. - If you study his strategy, you react better than him.

Meglio is an adverb meaning 'better' (the comparative form of bene, meaning 'well'). It is used here because it describes how you react (a verb). Migliore is an adjective (the comparative of buono, meaning 'good'), which you would use to describe a noun, like saying someone has a 'better strategy'.

Why use di lui for 'than him' instead of che lui?

When you are comparing two subjects and the second part of the comparison is a pronoun (like lui) or a noun, you use di for 'than'. You generally use che when comparing two verbs, two adjectives, or two quantities.

Doesn't sua mean 'her'? Why is it translated as 'his' strategy?

In Italian, possessive adjectives agree with the gender and number of the thing being owned, not the owner. Strategia is a feminine noun, so it must take the feminine possessive la sua, even if the person who owns the strategy is a man.

Why is the verb conjugated as reagisci instead of just 'reagi'?