It depends on the size of your flock and the personalities of the roosters. If you have just a few hens and a small enclosure, the likely hood of them fighting is definitely more likely. On the other hand if you have larger encloser, and a few more hens I'd give them a chance to get along. I currently have 8 hens and 2 roosters and they are fine around each other. It's clear one is above the other. They will develop a pecking order just like any other chickens. The older current rooster you have will want to maintain his position as flock leader. If the younger rooster falls in behind the older one it'll be just fine. On the other hand if the older rooster is say old enough to be past his prime, it's possible the younger one might eventually challenge it. That's when you have an issue is if the younger one challenges the older ones position as flock leader.
I have let my hens go broody and hatch a few times with that comes a mix. At one point I had 1 old rooster, 2 middle age rooster, and 2 more young roosters. Eventually there started to be issues between the 2 middles and the 2 youngest. The oldest one was an attack rooster and would defend his flock anything, so no one would challenge him, plus we let them free range during the day so I wanted him to continue to be around. Eventually we put the two middle roosters in the freezer and harmony was restored.
The moral of the story is that multiple roosters can definitely get along, but not always and my story of 5 roosters is no doubt extreme and not typical but it proves they can get along together. If it was me I'd probably keep them both at least for now. It can be difficult at best to rehome a rooster so I'd be inclined to just see how it goes. And then make a decision on which one to keep if they start having issues getting along.