I can't recall to the rule book anything on opposed rolls in general, however I can remember the rules for dodging. Dodging an attack is a kind of opposed roll, so I'll make a comparison based on that, which I hope will be helpful to you.
When a successful attack is made against a target who is dodging, the target rolls Dodge; if the roll is successful and is higher than the attack roll, the attack is completely dodged, and no damage is dealt. There's a little bit more to dodging, but that's the relevant portion for the purposes of my comparison to opposed rolls in general.
General Opposed Rolls
The "attacker" rolls their skill; if they succeed, the "defender" rolls their skill, and compares it to the attacker's roll. If the defender succeeds and rolls higher than the attacker, the defender "wins." Some noncombat opposed rolls can be difficult to determine who the "attacker" or "defender" is, and in those cases it should be a GM call. In general, the person who is acting first, being proactive, changing the status quo, or who would make their roll regardless of the rolls others may or may not make is the "attacker." (This puts Sneaky McSneak as the attacker in the given scenario.)
There are a few more things to consider:
- Fumbles: A character who fumbles fails at their task, and miserably so. If the attacker fails, there's no need for defense, so there's no worry here about both characters fumbling (the defender won't roll at all if the attacker fumbles).
- Failure: In dodging, the defender only takes half damage if the attacker rolls under the defender's Dodge skill, even if the defender fails the Dodge roll. This "half damage" concept doesn't really apply in most opposed situations, though.
- Matched Success/Failure: Matched successes and matched failures are often indicative of achieving a better result than otherwise, but a match does not guarantee a different outcome. If the attacker rolls 11 and the defender rolls 12, the defender still wins. Similarly, a matched failure is no worse than a normal failure when the result is a binary yes/no answer. (The most notable advantages of matched successes are with a combat-oriented obsession skill or with magic, which gets you cherries; the most notable disadvantage of matched failures is with magic, which gets you sour cherries.)
- Critical Success: Normally, a 01 produces an astounding success. However, it's also the lowest possible roll, meaning without being special, it's the worst possible result; so it does need special treatment. You shouldn't leave the defender zero chance of success if the attacker gets a critical success, but it also shouldn't be the X% chance they would normally have to succeed. I'll reiterate that I don't have the rules in front of me, but I would give the defender success on a Hail Mary roll if the attacker scores a critical success; that gives you a 2% chance at success with a 15 in the skill up to a 10% chance at success with a 99 in the skill. (In the 45-54 range, your chance at a Hail Mary is equal to that of a natural 20 in a d20 game like D&D.) If the defender is the one with the critical, he or she wins -- either they crit against a non-crit attacker, or the attacker crit and they succeeded at the Hail Mary.
- Minor, Significant, or Major: A minor check is an every day event that just about anyone with the skill should be expected to pass. Opposed rolls should not be minor. A significant check is one which is a challenge, however doesn't present danger or other great pressure. I feel that the mere fact that you're competing with another constitutes such pressure, meaning the opposed roll should not be significant. That leaves major checks, which alleviates one of the problems you considered (what to do with marginal success on significant rolls).