This is kind of a tricky question.
You are correct that DND doesn't have as much customization. A lot of character choices are kind of eclipsed by the big 1d20 random factor, too. Like, it doesn't matter a lot if you have +2 or +5 if you're adding 1-20 to it and looking for a result of 13. You're going to hit it a lot either way.
As to what you should play instead, that's really hard to answer from here. What is your group like? What do they want out of the game? Is it really a bunch of people who have never played anything before?
Personally, I really like Fate and think it's more intuitive. But it requires your players to be a little more bold and creative than DND. If you have a bunch of timid wallflowers it's not going to be great. But if you have a bunch of fun storytellers it can really sing. Also it's free and only uses standard d6 dice. But if no one's played anything before you might struggle, and might want to look into sourcebooks for sale.
Powered by the apocalypse games are also really popular. Some of them are meh, but that's sturgeon's law. They tend to be a lot more narrative and less concerned with "you can move exactly 15 feet".
Blades in the dark is also really popular. It's about heists. Pretty easy to pick up. Probably I'd recommend this one if the theme is interesting. It's a decent system and doesn't have any dndisms.
There's also a whole universe of dnd-likes, but to my knowledge most of them aren't different enough to be worth it. Most of them bring a lot of dnd-isms with a handful of tweaks. I don't see the point.
I personally really like the Chronicles of Darkness games. They can be a little crunchy, but I started them many years ago so they have a soft spot in my memories. If you wanted to play a game about being a vampire or werewolf or mage in modern day, they have you covered. They do require more reading and investment though.
Which goes back to not knowing your group. Most groups have at least one person who's not going to read or learn shit. Some have more. How many do you have?
Tldr: fate is awesome. Pbta is worth checking out. Blades in the dark is good.