Advantages of Ruby 3H vs Ruby 3?

I am wondering if moving from .3mV to .7mV will help reduce surface noise, "clicks" and "pops"? Will increasing the cartridge output allow volume/gain reduction from preamp while maintaining a similar SPL all while lessening the louder surface noises or will they remain unchanged?
How much performance is lost between moving from a .3mV to a .7mV Ruby? What would suffer the most speed, tonality, etc.?

It will have no effect on surface noise, clicks and pops. The differences between the two cartridges are very small if each is matched to an appropriate phono stage.
You will gain close to 12dB improvement in S/N ratio by increasing the output to 0.7mv but you will reduce high frequency extension a little bit but only at levels much higher than 20KHz. in other words, frequency may go up to 60KHz at 0.3 but only 50KHz at 0.7. You won't hear this easily...but you will hear a 12 dB improvement in S/N.

Go for the highest output available.
The reason for low output moving coils is that the coils are very light and have very low mass -- therefore, their transient response is faster than higher output moving coils that use heavier, more massive wire coils. Of course this will only be noticeable if your system is fast enough and resolving enough to show the differences.

For the best performance you should buy the lowest output moving coil cartridge that your phono stage can handle without becoming noisy. Some of the most prized moving coils are those with minimal coil mass and the lowest output.