The larger the number of ohms, the higher the resistance. More resistance results in less current flowing which means a dimmer led. When current passes through an LED, which is a diode, the voltage drops by some amount. This drop is referred to as the "forward voltage". The forward voltage value, along with the source voltage and the resistor value can be used to calculate the current through the LED using the formula I = (Vs - Vf)/R. The resistor is chosen to yield the desired current. Every led has a different forward voltage, but those with the same color tend to be similar.
Red LED usually have a forward voltage of about 2.0V while White tend to be around 3.3V. Therefore to keep the current the same, and therefore similar brightness, you need to use a resistor with a lower value. That being said, it would be safe to use the same resistors. The LEDs would just be dimmer.