In any fight it is best to know where the other guy is before he knows where you are. Strength and Dexterity are often prized above Awareness but really it's better to get the first shot in or even not to be seen. Awareness lets you do that.
In a fantasy setting the thief's backstab is his field leveler. While the rest of the party slugs it out toe to toe he pops up behind the foe and goes to work. How much more effective would he be with a pistol or a rifle?
Low (nearly superhuman. Think Tarzan or some other born in the wild type.) All of the character's senses are very acute. Any penalties for darkness or smoke are halved. In addition the character rolls with advantage for any rolls involving ambushes, surprise attacks and other enemy actions. In more dated terms the character will detect a secret door on a 1-2 as he passes by. Any rolls made against Awareness get a -2 bonus and many rolls such can be waved.
Paranormal (clearly superhuman. Think Wolverine from those Mutant Movies.) The character can see in all but absolute darkness. Hearing and other senses are 4-5 times as acute as normal. They can hear a whisper 10-20 feet away or feel the pattern on a dish. The character can smell lingering traces of chemicals and gets a roll for things like tasting poisoned or spoiled food before ingesting a dangerous amount. They are quite capable of sensing a truck or car coming by feeling the vibrations on the road they stand on. More telling the character has a good idea where people are going to look by reading their body language and rolls with advantage to remain unseen. Finally the character has a sort of sixth sense allowing him an Awareness roll to sense attacks coming from behind or from hidden enemies (like a sniper). The character detects secret doors on a 1-3.
Inhuman (high level superhuman. Think Daredevil but with 20/10 vision.) Many secret doors are no longer a challenge to the character who detects masterfully concealed doors on a 1-4. The character can hear people breathing at 30 feet, read print by touch and can appear out of nowhere to startle foes by making a Dexterity roll. In addition to the sixth sense the character appears to be a mind reader, often able to tell if a person is lying by their body language or pheromones with an Awareness roll. They can easily count the number of rounds fired off by a squad and tell which man is reloading.
Character's with heightened senses may be at a disadvantage in many situations. An artillery round going off nearby is much louder to them for example, strong odors can cause them to fall ill quickly, strong odors can sicken them. In situations like this they may have to make a Constitution roll, possibly at disadvantage for characters with higher levels of the power. Carrying welding goggles, earplugs and filter masks can allow them to make a normal or advantaged roll.