The higher value wins, regardless of acing.
Here are the relevant rules passages for trait rolls (which is what you mean when you say a skill check) and some observations about how opposed rolls (contests) work.
Aces (Savage Worlds Deluxe Explorer's Edition, p. 70)
All Trait tests and damage rolls in Savage Worlds are open-ended. That means that when you roll the highest number possible on a die (a 6 on a d6, an 8 on a d8, and so on), you get to roll that die again and add it to the total....
I'm omitting a little bit, but there's no indication of any special "critical" or "trumps" concept given. If you ace, you get to add the value onto your total result, but that's it.
Opposed Rolls (Savage Worlds Deluxe Explorer's Edition, pp. 70-71)
Sometimes rolls are “opposed” by an opponent. If two characters are wrestling for control of an ancient artifact, for example, they both make Strength rolls and compare results.... The highest total wins. In a tie, the two foes continue to struggle with no clear victor.
There's again no indication of any rules for who wins the opposed roll other than the one with the higher total. By omission, acing has no effect on that (except that whoever aces likely has a higher total).
It's worth noting that in Dungeons & Dragons 3rd, 4th, and 5th editions there is no such thing as a critical success on an ability check or skill check, through there is with attack rolls and (in some editions) with saving throws. Beware of trying to compare Savage Worlds concepts to D&D, but also beware of any "common knowledge" rules you've never actually read a rule for in any of the games you play. I'm not accusing you of anything, but just offering cautionary advice based on the comparison you used.