Which algorithm to use to match two categories with n dimensions
There is no generalized algorithm to match two categories of data where the dimension is different and perhaps the attribute could also be different. However you can transform the data into similar dimension. One method I would suggest you is to take PCA of both the data.  After taking PCA you can pick the first k principal component of both the data making them virtually identical data with similar attributes. Then you can use k-nearest neighbour on the transformed data of Aisles to train your model. The model could be easily used to test the transformed data of products.