I did a test with both cases and the performance was irrelevant, with small values, but memory lease is something that should be taken into account.

When you create the list with capacity 0 (zero), .NET will increase and allocate space dynamically as new items are added to the list, always doubling the previous capacity, power of 2. In practical terms, if your list has 2 elements and its capacity is 2, when adding one more element it doubles the capacity by allocating space for 4 elements. So long, but since it's exponential, when you have 64 elements and add one more, a capacity of 128 will be allocated, and so on. If you have 8192 elements and add another, the capacity goes to 16384 and so on.

With this we can conclude that from the point of view of space and memory allocation, it is more advantageous to define the capacity of the list if we know the size and it is large. How big is it? It would have to analyze the type of object that goes in the list to calculate the allocated memory, but something with more than 1000 items would already be interesting to define the capacity.

Here is a code that shows this:

```
System.Collections.Generic.List<int> lista = new System.Collections.Generic.List<int>();
Random rand = new Random();
int i =0;
while (i < 1000)
{
lista.Add(rand.Next(0, 20000));
i++;
Console.Write("\nTamanho: " + lista.Count.ToString());
Console.Write(" Capidade: " + lista.Capacity.ToString());
}
```

It can be run here: link

Output example:

Size: 31 Capability: 32

Size: 32 Capability: 32

Size: 33 Capability: 64

Size: 34 Capability: 64

Note that capacity doubles, and soon the space allocated in memory as well.

EDIT : I ran the same code in dotnetfiddle with 50,000, 500,000, and 1,000,000 items, without initializing the capability and initializing. Below are the results showing the difference in memory consumption. Once again, performance from the point of view of time / cpu was irrelevant:

```
+-----------+------------------+------------------+
| Itens | Sem inicializar | Inicializando |
+-----------+------------------+------------------+
| 50.000 | Memory: 512.23kb | Memory: 195.34kb |
+-----------+------------------+------------------+
| 500.000 | Memory: 4.01Mb | Memory: 1.91Mb |
+-----------+------------------+------------------+
| 1.000.000 | Memory: 8.01Mb | Memory: 3.81Mb |
+-----------+------------------+------------------+
```