Breakdown of Его брат сильнее, но он всё-таки упорнее его.
брат
brother
он
he / it (for a masculine noun) / it (for a neuter noun)
его
him / it (acc)
но
but
Questions & Answers about Его брат сильнее, но он всё-таки упорнее его.
Why use всё-таки here instead of just всё ещё for "still"?
While всё ещё means "still" in a sense of time (an action is ongoing), всё-таки means "still" in a concessive sense, meaning "nevertheless" or "all the same". Here, it highlights the contrast: despite the brother being stronger, he is nevertheless more stubborn.
The word его appears twice. Are they doing the same grammatical job?
No, they serve completely different roles here. The first его is a possessive pronoun meaning "his" (его брат = his brother). The second его is the personal pronoun он (he) declined in the genitive case, used here to mean "than him" right after the comparative adjective.
Could I say упорнее, чем он instead of упорнее его at the end?
Yes, both are perfectly correct and common. Russian allows you to form comparisons either by using the conjunction чем followed by the nominative case (чем он), or by skipping the conjunction and simply putting the object of comparison into the genitive case (его).
Does упорнее (more stubborn) have a negative connotation here, like being unreasonable?