Pragmatically, since both sentences are being figurative and hypothetical, they do mean the same thing. But the second sentence is more idiomatically correct and a better writing style. The first is unnecessarily convoluted.

They mean the same thing. Grammatically, they are different. #2 is better than #1. #1 is a compound sentence. Really, it is two complete sentences, each having its own subject and verb. The two phrases are linked by "if" acting as a conjunction. #2 is a single sentence containing a long adverbial clause, "to be able to ... one minute", which modifies the verb "give" by explaining "why I would give". #2 is superior to #1 because it links the two thoughts together ("giving anything" and the reason "to hold him...") more concisely and effectively and without cumbersome logic.

They both mean the same in daily colloquial speech. But there is a subtle difference. The first sentence is potentially more powerful, suggesting you would give everything you possesses and every last part of you, you would be willing to sacrifice yourself lay down your life, for a person or cause. Everything encompasses EVERYTHING not just physical possessions.. The second sentence ANYTHING tends to imply only physical possessions. but not anything of yourself you love dedication or devotion are not included in the second sentence. First sentence is for poetry literature and to expresses deep emotions. Second sentence is shallower in meaning and suggests only that you would give personal possessions but not necessarily all. People who say this do not always mean what they say. I would always use the first sentence.

Both sentences mean the same thing. They both express a strong wish and a willingness to sacrifice something precious for a chance to hold someone again. Here's a way to understand the small difference between the two: Imagine you have a big box of toys. Sentence 1 is like saying, "I would give away *all* my toys if I could have a hug from my best friend." Sentence 2 is like saying, "I would give away *any* of my toys if I could have a hug from my best friend." Either way, you're ready to give something valuable for that hug, and that's what both sentences are saying.

To point out the way this particular sentence is most commonly used in English art pop culture theatre etc please study the lyrics of this song "I would give up EVERYTHING I own just to have you back again. https://www.youtube.com/watch?v=b-CHW9jOfN0. The first sentence is so much better and more powerful to use.