Every applicative yields an arrow and every arrow yields an applicative, but they are not equivalent. If you have an arrow arr and a morphism arr a b it does not follow that you can generate a morphism arr o (a \to b) that replicates its functionality. Thus if you round trip through applicative you lose some features.
Applicatives are monoidal functors. Arrows are profunctors that are also categories, or equivalently, monoids in the category of profunctors. There is no natural connection between these two notions. If you will excuse my flippancy: In Hask it turns out that the functor part of the pro-functor in an arrow is a monoidal functor, but that construction necessarily forgets the “pro” part.
When you go from arrows to applicatives you are ignoring the part of an arrow that takes input and only using the part that deals with output. Many interesting arrows use the input part in one way or another and so by turning them into applicatives you are giving up useful stuff.
That said, in practice I find applicative the nicer abstraction to work with and one that almost always does what I want. In theory arrows are more powerfull, but I don’t find my self using them in practice.