We recently started feeding two stray cats in my apartment complex and initially they all behaved. However for the past two days one cat is trying to pick a fight and chase the other one away (the smaller one). The bigger cat is almost always near where we feed them. The smaller one actually disappeared for two days and returned yesterday where the big cat again tried to chase him up a tree and then stood there waiting at the bottom. They don't fight while eating. The bigger one typically eats faster and then goes after the smaller one. Am I causing this in some way? Are they competing over food? We usually give plenty to both of them. We used to keep a sizable bowl of dry food for them to nibble on when they are hungry again but it looked like nobody ate from it a lot and we stopped keeping that.
First of all, you are not the reason they fight. The cats are already competitors. By feeding them, they both have to be too close to each other and this causes stress for both cats. The amount of food is not an issue.
Both cats' lives have been dependent on their ability to keep other cats out of their territory to survive. This means you need to feed them in two places as far away from each other as possible, or at least out of sight of each other.
Undesexed male cats will be territorial. They will fight over resources and territory.
By limiting resources - not keeping out a continuous supply of feed, it just gives them another resource to fight over. However, as they get older the larger cat just may not want the smaller cat around, to share females with. So the food alone will not be the problem between them generally.
I'd suggest putting out a continual supply of dry food.
You can still offer the nicer food, but perhaps give the bigger cat a larger portion, to give the smaller cat time to finish eating. I don't know how close you are to these cats. If possible supervise them while they eat, or as suggested, feed them as far apart as possible.
Is it possible to trap them and have them desexed?
This will reduce the aggression between them.
Possibly keep one or both as a pet, which essentially you are, just not in the ordinary sense, of having them curled up on your keyboard.