In some cases“觉得”means a feeling,such as"我觉得冷"，in other cases it means a thought:"我觉得你是个好人"equal to"我认为你是个好人"，but"认为"is more logical,I think. "以为"means"I thought xxx,but I was wrong",such as"我以为天气冷，但其实天气很暖和"，and"我以为你是个好人，但你不是". But long ago in ancient time we used"以为"as"认为"，"吾以为，此事必有蹊跷"that means"我认为,这件事很可疑". That's my opinion.

First of all, the sentence of your question is not right there is no 為什麼....不都一樣? 1. 為什麼"覺得"和"以為"都一樣? ( why A and B are the same? ) 2. 為什麼"覺得"和"以為"不一樣? ( why A and B are not the same? ) 3. "覺得"和"以為"不都一樣嗎? ( you think they are the same, but people might not agree with you, so you ask why ) Back to your question 覺得 is you think 以為 is you thought

I'm not sure if I understand exactly or not. But in my opinion, your "jue de" may be right or wrong. Because it's when you see something, you know a little about it, and you think and feel. But "yi wei" here, is almost wrong. It may be never happened.