This is a tricky question for a number of reasons. Firstly, ‘smart’ can be defined in a number of ways. Secondly, it’s almost impossible to measure their ‘intelligence levels’. There’s no way I can say definitively that one was smarter than the other- they were both brilliant women. Nonetheless, I shall try. For the purposes of this answer, I am going to define ‘smart’ as cultural and ‘book’ smarts.
At the time of her reign, it could be argued that Anne was comparatively more cultured, having been served for an extended period in the French Court. As far as I am aware, Katherine never travelled abroad like Anne did. Both women were patrons of the arts and heavily influenced by fashion abroad (perhaps Anne more so- having spent so much time in France). Both women were multilingual, Anne is thought to be able to have understood Latin, as well as her being fluent in French. Katherine Parr was also fluent in French, as well as Italian and Latin. Upon becoming Queen she also took it upon herself to learn Spanish. Both Katherine and Anne were well known patrons of the arts.
Both women were well versed in religious doctrine for the time and the emerging new faith. Both were thought to be influenced by the ideas of Marthin Luthor and other scholars of the same period. Katherine was actually one of the first women in England to publish a book under her own name. By the time she passed away, aged thirty six, she had written three novels. Anne is well known for being one of the early reformers and I doubt Katherine would have been able to publish what she did if it were not for Anne’s earlier influence. It was Anne who had the courage and vision to champion the cause of Lutherism when the reformation was still in it’s infancy. It was the platform that Anne had assisted in creating that later gave Katherine her voice.
Both women were outspoken and headstrong. Politically speaking, I have to give Katherine the edge. I simply believe that she was better at handling Henry than Anne. I believe that Katherine was more pragmatic than Anne in her handling of Henry and tenure as Queen. She knew to submit to him
appeal to his ego would spare her imprisonment.
In short, after this long and rambling answer, I think that both women were spectacular in their own way (as were each of the wives) and it’s quite difficult to put them side-by-side and to judge them by the same standard.