Shearman & Sterling clearly states that if you have any upcoming internships to state it. It definitely applies to Vacation Schemes too. I would include it, especially if the firms are competing or are in the same category.
If the VS dates at the two firms would clash, then you would need to be careful. You could potentially play it to your favour saying "I got x, but I like your firm more so I would choose you over them" but that's tricky and I'd be cautious with it.
Finally, if the firms are not similar at all, then it is a matter of discretion. To see if they play off of each other well.
Overall, in most cases, I would personally include it.