Welcome to the forum, gad you joined.
How old are they? That can make some differences in how they interact, now and in the future.
What you describe isn't unusual. It's not that they don't like each other. When two males of a certain maturity meet in a flock they are going to decide who is the dominant flock master. Sometimes this means a fight to the death. Sometimes they reach an accommodation on how they are going to manage the flock. But they will know which one is boss.
What often happens is they they fight for a while but one decides running away is a better option. So if he has room to run away and get away they are much more likely to work out an accommodation than if they are trapped too closely together. How much room you have can make a big difference. I'm not talking about that silly 4 square feet per chicken in the coop and 10 square feet in the run in these circumstances but enough room to get far away and avoid the other. Preferable out of sight either because of distance or, because of clutter, he has something to hide behind.
If one can't get way but really wants to they will often lay down and protect their head. Pecking the head is a good way to kill another chicken, that's what they often try. That's a little unusual to me that your one just stands over the other and doesn't peck. He is demonstrating his dominance by pinning the other down. He won't suffocate the other, the danger is if he decides to peck.
Will one kill the other or will they work out an accommodation? I don't know.
You purposely brought in the new rooster. The only reason you need even one rooster is that you want fertile eggs. Anything else is personal preference. Nothing wrong with personal preference, I have a few myself. Why do you want two boys? What are your goals? What do your facilities look like? There are ways to manage that but it would really help to know your goals and what you have to work with to make reasonable suggestions.
Good luck and once again,