I recently watched a video with Ben Shapiro and Piers Morgan having this debate in 2013. You can see the video here: if you're interested.
Moreover, I have to admit that I was stumped a bit by Shapiro in this video. I also agree on a lot of what Shapiro says in the video.
According to statistics, it is true that the majority of murders in the US are committed by handguns; not assault weapons, which Ben also states in the video. And, here is a journalistic resource on it: https://journalistsresource.org/studies/government/criminal-justice/effectiveness-policies-programs-reduce-firearm-violence-meta-analysis
However, there have been recent mass shootings lately, with Vegas being the latest one. There were unfortunately 69 deaths. https://jamanetwork.com/journals/jama/fullarticle/2657418. Now compare that to 6,220 were committed with handguns in 2011. At the moment it probably does look like that handguns are more of a problem. But not so fast.
Let's just imagine that the 6,220 and 69 figures are within the same year and that the 6,220 figure is over a 12 month period. Now divide that by 12, you find you have the approximate 518 per month figure. Now divide that by 4 you then have the approximate 130 a week figure. Then divide that by 7 you have the approximate 19 a day figure.
Similarly, multiply 69 by 7 and you get you get 483 a week. Then multiply that by 4 and you get 1932 a month. Then times that by 12 and you get 23,184 every year. My point here is that assault weapons are capable of doing harm to thousands of more people than handguns, even though they may not be causing as much harm right now.
However, My current stance is for tighter control on handguns in the US and I don't think there is any need for assault weapons for either self-defense or to protect the constitution.