(1) Malliavin calculus has been used in mathematical finance to compute sensitivity parameters of option prices, see these <A HREF="http://www.math.wisc.edu/~kurtz/NualartLectureNotes.pdf">lecture notes</A> and this <A HREF="http://www.tandfonline.com/doi/full/10.1080/00949655.2013.814135?src=recsys">research article.</A>

(2)  Hida's white-noise infinite dimensional calculus relies on built-in spaces of stochastic distributions (Hida and Kondratiev spaces). The Malliavin calculus is more flexible, in that it allows one to build solution spaces optimal for the equation at hand. In <A HREF="https://www.jstor.org/stable/pdf/40484396.pdf">A Stochastic Modeling Methodology Based on Weighted Wiener Chaos and Malliavin
Calculus</A> this feature of Malliavin calculus was used to obtain more powerful numerical approximation schemes than would follow from Hida distributions.