I'll take the opposite stance.
The R44 is the better trainer, full stop. It's more stable, less twitchy, flies more akin to a 'proper' helicopter and is more forgiving of mistakes than the R22.
There are loads of PPLs out there who have successfully trained on the R22, and consequently sing its praises, but that doesn't make it a good training helicopter. Furthermore, the tricky nature of the R22 mean it's likely to take more hours to learn on than on the 44. My latest stude has just learned to hover unassisted in just over 1 hour on the R44. I've never had anyone come anywhere close to that in the R22. So I'd expect at least 10% less hours required to become competent on the R44 - my guess and based on experience and gut feeling, not hard fact. Finally, don't forget how the hour meters are wired on the R44 and the R22. The R22 uses an oil pressure switch so the clock starts ticking as soon as you turn the key. The R44 uses a collective lever switch so you only pay for the flying you do. So there's another 10% saved. (ask about this when you contact the schools and see how they work out their charges; they can vary school to school).
Finally, the old adage 'if you can fly an R22 you can fly anything' is also twaddle. As a learner, you will have to concentrate very hard in your first hours simply on controlling the helicopter. This means that you'll be using all your available mental capacity simply controlling the machine. In turn, it means that you won't be receptive to learning 'extra' information. If the machine is easier to fly, like the R44, you'll quickly develop the spare capacity to learn the 'extras'. Anyone can fly a helicopter by twiddling the sticks in the right sequence; the difference between a good pilot and a poor one is their extra knowledge and the ability to implement it effetively whilst twiddling the sticks. Do yourself a favour; ditch the R22 idea and stick to your guns and learn on the R44.
JJ
(edited for typos)