collaborative filtering using graph and machine learning
I can only speak about Graphs:

Advantages:


Using graphs, you can easily find products bought/rated by users that bought or liked an item, or users that have similar "taste" to another user. From my experience the traversal process is fast enough.
Closely matched products are easy to find, depending on how you model your graph: e.g. (userA)-[]-&gt;(basketA)-[with]-&gt;(productA)&lt;-(basketB)-[]-(userB). Finding similar products by basket is computationally cheap here


Disadvantages:


Depending on how you rank your results, you can easily run into the trap of constantly recommending the same products. Users that bought A, bought B. So you suggest B. People buy/like B. Next time you run the query, B will keep coming on top. 
Your results will rarely uncover new products. You'd have to find smart approaches around this, e.g. find other products, within this price range, with this category
If you have very large data sets, you'll have to use a distributed graph database that performs well (this is not as easy as it sounds, unless you're willing to pay large sums of money)


My little experience with ML for collaborative filtering, is that when your data grows large (50GB+), building a model takes a considerable amount of time (hours, days), and you're not likely to get good recommendations on new products. Having to update your model becomes a huge problem too. From my experience, I lean towards graphs for small use cases.

Note that for both cases, you never recommend newly added products that have not been bought or liked by someone. I say this because the goal of recommendations is to help users uncover new products. There is a blog post I wrote, where I talk about modelling graphs, and I discuss recommendations in some examples here, so you can skip to that section to get an idea on how to model this kind of problem.

I advise you to read up on Amazon's paper on their approach to collaborative filtering, which is pretty simple, in theory, and yields good results for them. I think you'd always want to implement a few different approaches combined, to tackle different parts of the problem.

Good luck.