If you are starting with something that has a .Length or .Count (such as ICollection<T>, IList<T>, List<T>, etc) – then this will be the fastest option, since it doesn’t need to go through the GetEnumerator()/MoveNext()/Dispose() sequence required by Any() to check for a non-empty IEnumerable<T> sequence.
For just IEnumerable<T>, then Any() will generally be quicker, as it only has to look at one iteration. However, note that the LINQ-to-Objects implementation of Count() does check for ICollection<T> (using .Count as an optimisation) – so if your underlying data-source is directly a list/collection, there won’t be a huge difference. Don’t ask me why it doesn’t use the non-generic ICollection…
Of course, if you have used LINQ to filter it etc (Where etc), you will have an iterator-block based sequence, and so this ICollection<T> optimisation is useless.
In general with IEnumerable<T> : stick with Any() ;-p