kate,
It is crowded! But if you adjust your brain before you go in, you can ignore people. Also, we made the mistake of going as soon as it opened in the morning, but that's when all the coaches arrive, so it might be better to go after lunch - it seemed less crowded, but perhaps we were used to it by then. And it's no worse than Hidcote.
So go and enjoy it, and don't forget to explore the village.