which thesis is better?

You should delete the word "I" in your thesis and I prefer your first thesis. Hope this helps.

2 word difference, either will work, but try:

Citizens should be allowed to buy fully automatic weapons because we live in a world with much hate and crime, an increasing number of illegal weapons going to the wrong hands, and fully automatic weapons provide extra security.

Well, for any thesis (or the entire essay), you usually don't use the word "I."

You are writing statements. And if you have an opinion, you'd usually write it in the form of a statement.

(Instead of "I think dogs are cute," you'd say "Dogs are cute.")

Theses are usually opinionated (and you try to prove this opinion throughout the essay), but are written in the form of a true statement.

So just take out the "I believe." (unless you were specified to write that!)

And I prefer the first one.

I would write this:

"Citizens should be allowed to buy fully automatic weapons because we live in a world with increasing hate and crime, illegal weapons going to the wrong hands, and for extra security."

Hope this helped!

Three pointers:

"I" should never be used in any thesis statement (or argument).

And since your paper requires a thesis statement, that means it's an argument. "I believe" doesn't create an actual argument.

You list "increasing hate and crime, illegal weapons going to the wrong hands, and for extra security." When listing items that are separated with commas, each part must start off with the same thing: either a verb, noun, or adjective. You could either do, "increasing hate, crime, and illegal weapons going to the wrong hands, and for the need for extra security." Or, "increasing hate and crime, continuing illegal weapon obtainment, and lacking domestic security."

Hope it helps.

Teachers would prefer choice one.