Both are good for disputes too, along with White & Case. However, all 3 firms are transactional focused (as are their TCs), so if you apply to them, I'd be careful about how much you specify an interest in disputes.
In my opinion,
Skadden, Quin Emanuel and
Gibson Dunn are the best for disputes as they're highly ranked across different types of disputes around the world (commercial litigation, international arbitration, white collar, competition litigation etc). The Legal 500 USA and Chambers USA are great resources to see which US firms are the best at disputes (the disputes might not be London centric but at least you'll be working on top level disputes work).