You are most likely asking about when these are used as special verb particles, which function more like our tenses in English. (Because "過“ can function as a normal standalone verb also.) 了 indicates a state change, or something that is in the past already (which is also a state change in teh past, if you think about it). I think of 了 as equivalent to the "now" in a sentence like "It's raining now" (下雨了！） verb＋過 means to have "passed through the experience of doing it before", 我吃過 = I've eaten it before, I've had it before, 我去過， I've gone there before. 我看過 I've seen it before. Both can be used together, for example, if someone hands you a book you've already read, you can say, "看過了" = I've seen it already. (literally, I have had the experience of doing that before) let me know if this helps, or which parts are still unclear, I can give you my perspective on it... there are probably articles on the web which explain it much more clearly than me... these things are a key part of basic mandarin competence, and don't have exact equivalents in English, so once you learn these well, your Chinese skill will greatly improve!

过(guò) seems like "used to be ", it shows a kind of experience and some states before. For example, 我去过长城 shows that you have an experience to go the Great Wall. however, 了(le) is also used in actions in the past, but it just shows a matter of fact. For example, 我去了长城 shows that I went to the Great Wall, but now I am back.

I have a simple rule: 过 indicates "ever", 了emphasize "already"。...过了means“Ever done it already”

Anyway, the best answer is the best. Well, I remember a special case. 最好的答案的确是最好的。对了，我还想起一个特殊的例子。You already knew it, right?