Both are correct. "Spent" is probably more common, but "had" may be better, as a reply to a question that uses the same verb, e.g.:
A: What was the best moment you had with your father?
B: My best moment was every moment that I had with my dad.
Beyond what is correct and natural, there is good English writing/speaking style. As in any language, some people can do it well, and some can't. There are good writers and bad writers, good speakers and bad speakers. Some people can say something clever very quickly, "off the cuff", and some can only be clever when they have time to sit and write it down.
It's good style to mirror the general form of the question asked, but with a wry, humorous, or insightful twist. Your first example is somewhat like this, where the questioner expects you to respond with one or perhaps a couple of anecdotes, but the response is unexpected but sweet.
Of course, the trick about being clever is that you have to be original. This kind of twist ("every moment is the best") has been done so many times it's pretty much cliche. It's also not a real answer to the question. If you really want to sound clever, you might have to dig a little deeper:
A: What's the best moment you had with your father?
B: The best moments are the ones I'd nearly forgotten about, until something passing -- a smell, a flash of color, a word -- sparks the memory, and I'm back reliving that moment with him, as if it was that very day.