They're both "price", but I don't see the difference. Even the Kanji appear to suggest similar meanings. Thanks for any advice!
"値段" (mixed kun-on compound) is a rather colloquial word, used in most part of our daily life. In most cases, 値段 refers to "how much we/you have to pay" in individual transactions, from the viewpoint of those who buy or sell the item.
Using 価格 in casual conversations like these is not incorrect, but sounds a bit unnatural to me.
On the other hand, the usage of "価格" is that of typical 漢語. In serious written articles or business conversations, we mainly use 価格:
価格 can construct many longer compound words, such as 希望小売価格, 市場価格, 価格調査. I can't think of similar compounds which contain 値段.