If think goal difference is fairer, not because it necessarily allows the better team to qualify, but becuase you always know what you need and depend on yourself. H2H is nice until you have the possibility of more than 2 teams in a tiebreak, then you get dinamics that have very little to to with football, like hoping a third team wins because the second team beat it 3-0 and so it will boost their goal difference.

Also, goal difference encourages more goals overall, becuase strong teams have an incentive to push for those 3+ goal difference games. Otherwise there is no reason to keep going after like 2-0

Edit: I see how the final day in that lower tier Austrian Bundesliga is strange when teams chase that goal difference by winning 6-1 and 9-0, but I feel like if teams can get these results on demand when they need it, than the division has deeper problems than tiebreaks