Both are correct and mean the same thing, but the latter sounds much better to me. I think the problem is that such as is most often grouped together so it sounds a little strange when it is separated.
You have a small semantic issue though. I would say that Audi and Lamborghini are car manufacturers in this context. Although cars are often referred to by their manufacturer's name, the cars themselves don't grow.
[The company] has grown to compete with [other companies] such as [CompanyX]
[The company] has grown to compete with [cars] such as [CompanyX]
Audi has grown to compete with car manufacturers such as Lamborghini.