The Vinland Saga anime is well made. Wit Studio handled the first two seasons and did not embarrass themselves. The fight choreography in season one holds up. The voice acting is good. The transition between seasons, which covers a significant shift in tone, is handled without the whiplash I expected going in blind. I watched all of it and I would watch more.
I also read the manga. All 200-plus chapters, over about six weeks, mostly on trains. And the manga is better. That is my position, I am aware it is a minority view outside manga-specific communities, and I want to actually explain it rather than just say it.
The specific thing is how violence accumulates on the page versus on screen. Makoto Yukimura is not gratuitous, but when a character gets hurt in the manga, you see it build across panels in a way the anime tends to compress or cut away from. There is a stretch in the Farmland arc, around chapter 60 to 65, where the aftermath of a prolonged fight is given five full pages. The anime condenses that to one scene. I cannot say with certainty whether that is a budget decision or an aesthetic one. What I know is that the manga version made me put the book down and sit with it for a moment, and the anime version did not.
The anime has a real advantage in the score. Yutaka Yamada composed it, and there are sequences in season one where the music is doing structural work that the manga cannot do because manga is silent. The raid sequences in particular have a momentum that comes almost entirely from what is playing underneath them. That is not a small thing.
Where the manga wins clearly is the Farmland arc. It is roughly a hundred chapters of farming, a deliberate shift away from combat, and it requires spending time with people doing ordinary work and having slow conversations about theology and what a life is for. The anime adaptation compresses it. You feel the compression. Things that built over three chapters in the manga get a single scene in the anime, and the weight does not transfer cleanly.
I talked to someone who watched the anime first and then could not get through the manga version of that arc because it felt too slow. I read the manga first and found the anime version too fast for the ideas to land. We watched the same adaptation of the same events and had opposite problems with it. Neither of us was wrong about what we experienced.
The honest answer is probably that they are different enough to be worth doing both, in whichever order suits you. But if I could only recommend one starting point, I would say the manga. The anime is an adaptation that makes choices, some of them good, about what to keep and what to cut. The manga is the thing those choices were made from.
One more thing worth noting. Yukimura has been publishing Vinland Saga since 2005. The current arc is doing something structurally unusual that I find more interesting than anything that came before it, and the anime will not catch up for some time. If you want to see where the story is going right now, the manga is the only option. That is not an argument for the manga being better. It is just a fact about where the story currently lives.