On the Galaxy S3, there is no mute switch. I use a widget to adjust the sound settings on my phone. I find the widget I use is much more flexible than the mute switch on the iPhone.
One thing that I am not satisfied with the iPhone volume controls is that there is no easy way to mute notifications, but leave the ringer and alarm unmuted. I had to ask my wife to mute her phone when we go to sleep because her notifications disturb me and wake me up. However, she want to keep the ringer on. The iPhone volume level controls changes the ringer as well as notifications. We ended up settling on muting, but leaving the vibrate on when muted. When the phone rings, we figured that we can hear the vibrations while it is resting on the night table. Sometimes the vibration from notifications still disturb me, but it is not so bad as it goes away quickly.
In comparison, I use a widget on my GS3 to control my volume levels. The widget I use is called Volume Widget by Leep Studios. This widget allows me to set 3 different sound profiles. Each profile I can choose a different level for ringer, notification, media, alarm and voice. For my "sleep" profile, I have notifications off while my other sound levels are rather low. I have a "normal" profile where all sound levels are roughly medium and a "loud" profile where everything is maxed. I can change to each one by tapping on the widget. It requires waking/unlocking the phone and tapping on the widget, but I find the added flexibilty a good tradeoff.
By the way, if anyone can tell me how to do the same conveniently on the iPhone, please let me know. When I mean conveniently, I mean something my wife is willing to do. The only way I can find to leave the ringer on while muting notifications is go into every type of notification and muting it. That is too incovenient even for me.