I'll list out the similarities and the differences here. To give a caveat, I do know more about human design than I do about astrology. But here is the comparison that I'm aware of thus far.
The similarities
They both use your birth date information to draw up your chart and analyze the characteristics and tendencies that you have been gifted with at birth.
They both speak to characteristics that are "good" and "bad", which is subjective of course, but both systems do not shy away in the name of spiritual bypassing or in the name of toxic positivity.
Both systems can offer insights into your energies that can help you in practically all areas of your life, including romance, relationships, career, marketing, business, physical health, natural talents, and compatibility with other people.
They are not separate systems entirely. Astrology is embedded into human design. Both systems include the meanings and the positions of the planets in our solar system (Sun, Earth, Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto) as well as the North Node, South node, and Chiron. As you can see in the symbols on either side in my chart below.
The differences:
Astrology takes the snapshot of the planetary positions at the moment of your birth. Where human design does the same, but includes a snapshot exactly 88 days prior to your moment of birth as well. Human design then creates a single chart that overlaps these two snapshots. This is why you have two columns with the same planetary symbols on the human design chart above. The theory in the human design system is that the snapshot that was taken 88 days prior to your moment of birth represents the unconscious energies that are vibrating out of your physical body, whereas the snapshot of your moment of birth is how your mind and your consciousness operates. As you can see in the image above, the representation of the energies from the moment you were born are in black and listed along the planets on the right side of the chart. The representation of the energies from 88 days prior to your birth are in red and listed along the planets on the left side of the chart.
The benefit of having the insight into your unconscious energies is that it will help you to identify the behavioral patterns or relationship patterns that you seem to keep finding yourself in. We can only heal or transform what we are aware of. Human design helps you to see what's going on with you and the energies that your body emanates, including the type of people that you seem to attract, the situations or ways of thinking that you tend to gravitate towards, Etc.
The human design system does not use a house system like astrology does.
Human design gets into the specifics of the gates when it comes to transits. For example, if the Sun is in Gemini, Human Design goes it into the five specific gates that the Sun transits through Gemini. The image below is what we refer to as a mandala.
The hexagram symbols with the full and broken lines are representative of the gates. The hexagrams come from the ancient Chinese i-Ching. In Human Design, we call them gates. This mandala image assists us with giving the actual number of the hexagram/gate. For example, if you look in the top left of the mandala, you will see the number 1, and the associated hexagram symbol right beside it, and you see that it is a Scorpio gate. This means that when we are in Scorpio season, the sun transits through gate 50, gate 28, gate 44, Gate 1, Gate 43, and Gate 14 - because the Sun and the other planets move counterclockwise around the mandala.
In conclusion
I know many people who use both systems to support their healing and evolution. They are both fantastic systems that can support people to identify their true life purpose and become the people they were born to be. And human design, the theory is that the more we live in accordance to the way we were designed at Birth, the more we will experience a fulfilling life where we have the opportunity to contribute what we were born to contribute and what we are naturally talented in, and we get to receive an experience the things we were supposed to experience in this lifetime.