Food Causes Fights.
Dogs are extremely protective over their food. If a new dog comes on the scene, your existing dog may feel insecure about its food supply, especially if the new pup sniffs its food. By feeding the new dogs separately, you are showing your existing dog that its food supply is safe.
The Dogs Will Need to Integrate at Some Point.
Eventually the dogs will learn to accept each other and will be secure about their food source. The quicker this happens the better, but separate feeding will slow the process down. Two feeding sessions is hardly convenient for you, so if you chose to feed the dogs together, supervise early encounters to prevent fights.
Dogs all behave differently around food. Some become aggressive while others are submissive. If your existing dog is timid, gradually introducing the other dog at meal times is a good idea. If your current dog is confident, allow the two to eat together. The pup may learn the meal time boundaries quicker this way.