Fun question!
Dogs are better at hearing than us because their ears proved essential to their ancestors survival (as well as their ability to smell).

Anatomically (physical traits), dog ears are made up of 18 muscles, while human ears only have six. These extra muscles mean that dogs have greater control over how their ears move (so they can point them towards the sound source), where humans can only move their ears slightly (we generally move our head). This means that dogs can tilt and rotate their ears to funnel sound into the inner ear more efficiently. Additionally, the shape of some dog breeds ears (the outer part) are made to better amplify sound, just like when people hold their hands up to their ears to try and hear something better.

Finally, a dog’s ear canal is considerably longer than human's, which helps to more accurately discern sounds. A dog’s cochlea, which is a part of every mammal’s inner ear, makes 3 1/4 turns compared to the 2 1/2 turns in humans. These extra turns are thought to improve hearing of dogs.

Humans hear between the frequencies of 20 Hz and 20,000 Hz; with 2,000 Hz being the level we hear best. Dogs can't hear quite as low as we can -- their range begins at around 40 Hz -- but dogs can hear up to 60,000 Hz. A dogs best hearing occurs at 8,000 Hz. Dog whistles, which have really high frequencies, are above our range of hearing but in a dog’s range of hearing.

The reason that dogs can hear higher pitches is that their ears are shaped differently from human ears, though the exact range of a dog's hearing depends on its age and breed. Generally speaking, though, dogs have more muscles in their ears than humans do, along with longer ear canals, and the ability to move their ears. All of these factors combined mean that dogs' ears can receive and amplify (make louder) sounds that humans would not be able to hear, which is why they can hear higher pitches.

As for eyes, compared to humans, who have three different types of cells in their eyes with which to see color, dogs have two. The three types in humans allow us to see blue, green, red, and any combination of those three, resulting in the rainbow colors that we can see. In dogs, one of the two types of cells is similar to the type in humans that see blue light, the other type falls between red and green. This means that dogs see shades of yellow and blue, in addition to black and white.

This is cool. I never would have guessed that it's the outside part of dogs'ears that let them hear higher pitches than we do:

"The real key to better hearing in dogs is the 18 or more muscles that control a dog’s pinna, or ear flap. These numerous muscles allow a dog to finely tune the position of his ear canal to localize a sound, hear it more accurately, and from farther away. For this reason, dogs with upright ears, such as terriers, tend to have superior hearing to dogs with floppy ears, such as hounds. It also means that dogs are much more sensitive to loud noises than are humans. Loud noises that are tolerated by humans may be scary or even painful to dogs." hearing in dogs

Color vision comes from cone cells in our retinas - the backs of our eyes. We have 3 types of cone cells that see 3 colors and all combinations of those colors. Dogs only have 2 types of cone cells, and they don't have as many cone cells as we do, so they see fewer colors, and those colors don't look so bright. But dogs' eyes have more rod cells than our eyes do, so they can see in dimmer light, and they can detect motion better than we can.

Here's the website, and it has cool diagrams of the colors we see and the colors dogs see.
dogs vision

" Dogs are near-sighted creatures and do not see clearly at distances of more than 20 feet. So, while they are able to detect movement at great distances, they don't have the ability to differentiate between a person and a small tree."

Thanks for your question. It was fun to learn this stuff.

Dogs have red-green color-blindness. This means that they can easily see blue and purple and tell them apart from the other colors, but they have a hard time telling green, yellow, brown, and red apart.

Read a great answer for this question on the next link:
dog-hearing-vison

Sound is caused by vibrations in the air or in a fluid, and a higher pitch means that the air is vibrating at a higher frequency. Before dogs were domesticated by humans ~15,000 years ago, they were hunters , and having good hearing enabled them to find prey rustling in the brush. Ears are specialized to be able to convert these vibrations into electrical signals that can be interpreted by the brain, and dog's ears have evolved the ability to perceive higher pitches than humans. Inside the ear is a snaillike cavity called the cochlea that is filled with fluid and lined with hair cells . These tiny hairs can detect vibrations and convert them to electrical signals that are transmitted to the brain. The cochlea in a dog’s ear has more spiral turns and is covered with more hairs than a human cochlea. Having more hair cells means that dogs can detect sounds better than humans.

Most vertebrates other than mammals have excellent color vision. This includes birds, fish, insects, amphibians, and reptiles. However, around the time of the dinosaurs, the mammals from which today's mammals are descended, lost the ability to see red. Precisely, they lost the red cones in their retina. So dogs, like most mammals are called dichromats, meaning that they see only two types of primary colors (green and blue). This means that dogs have poor color vision, but they see some color. Dogs see mostly greys and some blues, greens and yellows, but not reds or oranges. Interestingly, during evolution, primates (monkeys) regained the ability to see the reds.

Primates are unique among placental mammals in that they are trichromats, meaning that they can see three types of primary color (blue, green, and red). There is a theory that color vision evolved in primates to help them find ripe fruit to eat in trees. Color vision is an evolutionary advantage to these animals because their diet is fruit. When a fruit is ripe it turns color, and so animals that can see in color are able to find ripe fruit easier. Since humans are descendants from primates we have inherited trichromatic color vision. However, some people are "color blind," which usually means that they have trouble distinguishing certain colors, most commonly red/green.