Well, if the amount they're paying for the phone is more than your iPod is worth, I see no reason why you should convince them. They don't owe you anything. Really, it seems they're not buying you a phone, but contributing an amount towards it (cost of phone - how much your iPod is worth). So there should be no reason to convince them, be grateful.
As you said, the games and music player really don't compare to their counterparts on iOS, for that reason I wouldn't want to give up iOS. If you can work out a deal to get an iPhone, I'd say take it. You'll only have one device in your pocket and you can keep all your App Store purchases. You wont be missing out on much by not using Android, unless you have some kind of obsessive compulsion to customise the hell out of your device 😛