Basically, they are same , but if you put them into different contexts, the two have slight different. For example, if someone asks "你吃早饭了吗？" The answer should be "（是的）我吃早饭了“，but not“我吃了早饭” if someone asks"你吃饭了吗？“ The answer could be "我只吃了早饭（I only had breakfast, no brunch, no high tea, but maybe it's 6pm now)” Hope this helps.

verb + 了 = The past tense so, 吃了早饭 = had breakfast 吃早饭了 has two possibilities: 1) present perfect. 吃早饭了 = have had breakfast = 吃了早饭了 2) imperative sentence. for example, when a mom has finished cooking and she wants to call her children to have breakfast, she could yell: 吃早饭了！ in this case, 了 has no meaning, it's just a word to express some emotion. Here, it tells us that this is a kind of order.

On their own as standalone sentences there is not really any difference. However depending on what comes before or after them the meaning could change.