You can use const variables as input to attribute constructors but not readonly variables.

Example:

public static class Text {
  public const string ConstDescription = "This can be used.";
  public readonly static string ReadonlyDescription = "Cannot be used.";
}

public class Foo 
{
  [Description(Text.ConstDescription)]
  public int BarThatBuilds {
    { get; set; }
  }

  [Description(Text.ReadOnlyDescription)]
  public int BarThatDoesNotBuild {
    { get; set; }
  }
}

They are both constant, but a const is available also at compile time. This means that one aspect of the difference is that you can use const variables as input to attribute constructors, but not readonly variables.

Example:

public static class Text {
  public const string ConstDescription = "This can be used.";
  public readonly static string ReadonlyDescription = "Cannot be used.";
}

public class Foo 
{
  [Description(Text.ConstDescription)]
  public int BarThatBuilds {
    { get; set; }
  }

  [Description(Text.ReadOnlyDescription)]
  public int BarThatDoesNotBuild {
    { get; set; }
  }
}