When two sets aren't being drafted together, I generally don't find it very helpful to compare one to another. For example, if someone had asked how Adventures in the Forgotten Realms would differ from Strixhaven, I'd suggest that grounding themself in Strixhaven as a point of comparison is more likely to lead to carrying over baggage unnecessarily than simply starting fresh (unless Strixhaven was the only previous set they'd drafted). However, when it comes to this pair of Innistrad sets, I think the thematic and mechanical overlaps are strong enough that many players won't be able to help drawing comparisons, so let's dive into how they compare.
My top-level first impressions are that the commons in Innistrad: Crimson Vow look weaker; the removal's more expensive and/or less versatile and there's much less built-in card advantage. I think the fixing is a little weaker overall, particularly because almost all of it costs exactly three mana, which makes the curve harder to manage in decks that are trying to splash. Also, there are only ten uncommon gold cards instead of twenty, making fixing less structurally important.
On the other hand, Blood tokens offer cheap card filtering, which can make splashing much less painful, since you can just discard cards you can't cast, or dig to find your missing colors, which should make splashing easier in decks that are less invested in it, which is to say that compared to Innistrad: Midnight Hunt, we can expect green and blue to splash less and red and black to splash more.