Here is some data comparing the two methods (Convert... and Cryptography...). I ran 200 tests of writing out 1 million bytes to a new 1 MB file. It looks like the Convert.ToBase64 method is around seven times faster than the Cryptography method on average. The histogram of the test runs is below:

If anyone is interested in verifying my results - here is my test code:
private static void Test()
{
Random myRand = new Random();
List<TimeSpan> convert64Times = new List<TimeSpan>();
List<TimeSpan> cryptoTimes = new List<TimeSpan>();
Stopwatch theTimer = new Stopwatch();
for (int i = 0; i < 200; i++)
{
byte[] randBytes = new byte[1000000];
myRand.NextBytes(randBytes);
string filePrefix = @"C:\Temp\file";
// test encode with convert to base 64
theTimer.Start();
EncodeWithConvertToBase64(randBytes,filePrefix+i+"convert.txt");
theTimer.Stop();
convert64Times.Add(theTimer.Elapsed);
theTimer.Reset();
// test encode with crypto
theTimer.Start();
EncodeWithCryptoClass(randBytes,filePrefix+i+"crypto.txt");
theTimer.Stop();
cryptoTimes.Add(theTimer.Elapsed);
theTimer.Reset();
}
}
private static void EncodeWithConvertToBase64(byte[] inputBytes, string targetFile)
{
string fileString = Convert.ToBase64String(inputBytes);
using (StreamWriter output = new StreamWriter(targetFile))
{
output.Write(fileString);
output.Close();
}
}
private static void EncodeWithCryptoClass(byte[] inputBytes, string targetFile)
{
FileStream outputFileStream =
new FileStream(targetFile, FileMode.Create, FileAccess.Write);
// Create a new ToBase64Transform object to convert to base 64.
ToBase64Transform base64Transform = new ToBase64Transform();
// Create a new byte array with the size of the output block size.
byte[] outputBytes = new byte[base64Transform.OutputBlockSize];
// Verify that multiple blocks can not be transformed.
if (!base64Transform.CanTransformMultipleBlocks)
{
// Initializie the offset size.
int inputOffset = 0;
// Iterate through inputBytes transforming by blockSize.
int inputBlockSize = base64Transform.InputBlockSize;
while (inputBytes.Length - inputOffset > inputBlockSize)
{
base64Transform.TransformBlock(
inputBytes,
inputOffset,
inputBytes.Length - inputOffset,
outputBytes,
0);
inputOffset += base64Transform.InputBlockSize;
outputFileStream.Write(
outputBytes,
0,
base64Transform.OutputBlockSize);
}
// Transform the final block of data.
outputBytes = base64Transform.TransformFinalBlock(
inputBytes,
inputOffset,
inputBytes.Length - inputOffset);
outputFileStream.Write(outputBytes, 0, outputBytes.Length);
}
// Determine if the current transform can be reused.
if (!base64Transform.CanReuseTransform)
{
// Free up any used resources.
base64Transform.Clear();
}
// Close file streams.
outputFileStream.Close();
}