I am using another of the same type of LED...
If you are using the exact same part number, it should be about the same brightness.
...and 300 ohms ...
Lower resistance will give you more brightness, but you cannot exceed the current rating on the LED (typically 20mA) or the current rating of the Arduino output. LEDs are "constant voltage" devices (variable current) and you need to know the voltage before making any calculations.
LEDs are typically rated at about 2V (you have to check the spec for the particular LED). So, if we assume 5V out of the Arduino and 2V across the LED, that leaves 3V across the resistor. Using [u]Ohm's Law[/u], you can calculate the desired resistance (or current through a known resistance). 3V across 300 Ohms means you have 10mA through the resistor (and through the LED). If you wanted to calculate the resistance for 20mA, Ohm's Law gives you 3V/0.020A = 150 Ohms.