I'm actually not too sure about this in terms of it being a better or worse method of euthanasia. Helium is less narcotic than Nitrogen which makes it better for deeper diving than Nitrogen. However, as a result, helium does not induce narcosis which is unconsciousness from a narcotic. Nitrogen, on the other hand, can induce narcosis when divers dive too deep. It's similar to being drunk, really.
Essentially, there is little difference between CO2 and Helium in terms of suffocation as both create oxygen deprivation. The only difference would really be the process by which the gas asphyxiates (sp) the organism.
See, CO2 makes "stale" air in your lungs and it interrupts the breathing process because CO2 passes from the blood to the air so when you put back in what your body is trying to put out, you suffocate.
With Helium, Oxygen is actually removed from the blood stream during the breathing process. So, instead of just not being able to breath, it actually is taking Oxygen from your blood stream- something CO2 does not do. The usual result is an uncontrolled fall that can cause serious injury, even if normal breathing resumes before brain damage occurs due to lack of oxygen.
It's arguable as to which causes unconsciousness or death faster. I guess it all depends on how well your blood supply is oxygenated at the time of suffocation.
Little chemistry lesson for the day!

It's the best way I can explain it without drawing out the actually isotopes and gas exchange rates. Lol. Sorry!