I think Brighton performance is much better when compared to Ajax in terms of squad, although Ajax will play at home, but that wasn't enough for him to win against Brighton but it is possible that Ajax will maximize the draw.
Yes, you are right, sometimes as a home team it doesn't really matter when there is quite a big difference between the two teams in terms of strength and performance in that season, and as you said, there is a big difference in terms of performance between Ajax and Brighton, so it looks like Brighton won't face any problems when against Ajax and the betting market predicts the same thing by placing the away team as favorites to win the match in the middle of next week.
However, sometimes there are still doubts about Brighton because this season, at least in the local league, they lost by a landslide score, and also in the European league, in the first match, they lost at home against AEK Athens, so Brighton is not that strong, in my opinion, there is even a chance of a surprise happening in this match.
When you think about what Brighton has achieved, it's really unbelievable how far they have come and how good they have became in the recent years. This team wasn't anywhere near this level just a decade ago, and suddenly they have made themselves a very good team at premier league. They are aware that they can't fight against big clubs that have endless pockets, but they realized they could use the amount of money they are making at premier league, which is definitely more than what teams at other leagues makes, and they could use that to pay players accordingly and build a squad that could be at European competitions and do fine there.
Europa is where they can shine a lot, become the Sevilla of Premier league basically. This required a lot of amazing management decisions of course, but wasn't an easy decision, has to be a very tough decision making process for each time since they do not have any chances to make a mistake, it would be hard to comeback from even one mistake.