Consider a function which returns two values. We can write:
// Using out:
string MyFunction(string input, out int count)
// Using Tuple class:
Tuple<string, int> MyFunction(string input)
// Using struct:
MyStruct MyFunction(string input)
They each have their pros and cons.
Out parameters are fast and cheap but require that you pass in a variable, and rely upon mutation. It is almost impossible to correctly use an out parameter with LINQ.
Tuples make collection pressure and are un-self-documenting. "Item1" is not very descriptive.
Custom structs can be slow to copy if they are large, but are self-documenting and are efficient if they are small. However it is also a pain to define a whole bunch of custom structs for trivial uses.
I would be inclined to the custom struct solution all other things being equal. Even better though is to make a function that only returns one value. Why are you returning two values in the first place?
UPDATE: Note that tuples in C# 7, which shipped six years after this article was written, are value types and hence less likely to create collection pressure.