As an American who first visited Vietnam in 2016, I've had the opportunity to visit both of these cities as well as most of the entire country, traveling to 60 of 63 provinces to date. I've been to Hanoi probably 25 separate times and Saigon around 15 times. So I've done both over the course of multiple years and in different seasons. These are my personal observations, which I hope will help you make a decision as to which one to visit if you cannot visit both.
While both have their certain charms and character, Hanoi is the better place to visit if it's your first time to Vietnam and you have a limited amount of time to spend in the country. Disregarding the old-world charm of Hanoi's Old Quarter, there is simply more things to do in Hanoi than in Saigon, and there are many more sites and areas to visit within hours of Hanoi if you want to see more of the country side and other high profile tourist sites. Within 3-4 hours from Hanoi, you can visit TWO UNESCO World Heritage sites, Ha Long Bay & Ninh Binh. You can also get to the famously photographed rice terraces of Sapa, in northwestern Vietnam, or to the incredible mountain terrain of the Ha Giang province north of Hanoi within a couple of days if you want to have more of an off the grid Vietnam experience.
Saigon (Ho Chi Minh City) has a larger variety of Vietnamese foods that come from all around the country in my experience. You can also get more international foods from around the world in Saigon, as it has a long history as a major trading route in S.E. Asia. Hanoi cuisine is more specific northern Vietnamese foods and tastes that were originated in the region, and where they are still served on the sidewalks by street food vendors, many of whom have been serving the exact same food in the exact same spot, literally for generations.
Finally, from a cultural standpoint, Hanoi has a tighter, more conservative culture than Saigon. That being said, both cities are generationally more conservative than the USA and most western countries. Hanoi specifically though, has the feeling of a city that has pushed back against the march of time, and in my opinion is what makes it the best city to visit in Vietnam.
