I'm adding to this thread because I've recently switched to an S4 from an iPhone5 and been experiencing some of these problems.
Yes, it is completely possible to continue to group message with all of your iphone user friends, exactly the same as you did on an iphone, in exactly the same way. Start a new message, select your recipients, and off you go. Theoretically, all messages SHOULD come back in the group chat. There are some hiccups with this though, that could be attributed to several different things.
First, like many have stated, make sure to turn imessage off on your iPhone. It's important to do this before you do anything else with your phone. Restoring it to default and handing it over to a family member/friend, etc, does not turn off the imessage on your account. It's still there floating around in apple land. =) In fact, I'd recommend turning off everything relating to your apple ID on your phone before doing anything else. In the apple ecosystem, everything is tied to your apple ID (which I know is how it is with other platforms as well), so your number could technically stay associated with your imessage account. Some people have had to go through drastic measures to make sure their phone number isn't associated with their apple ID, but follow the steps from the least drastic first. Sign out of all info on your phone before restoring it to default. If you're still having trouble, then go to the apple support page and deregister your device (even if it's a phone you're keeping for later use, it's a snap to re-register it). In fact, I'd recommend de-registering it anyway. It just makes sense. If that still doesn't work, go to your other apple devices (if you have any) and make sure the iMessage apps don't still have your number listed in there (they would be in grayscale). If they do, then the next thing I would do would be to unregister those gadgets as well, then change the apple ID password, then reregister the devices. This includes any spouse or family member with an idevice that shares an apple ID with you. This really doesn't take as long as it sounds, and remember, only try each step if the previous step doesn't work.
Hopefully that will help. If there are any other issues, it must be related to some highly technical giltch that will be a major pain to sort out. =/ I'm currently having trouble with group chat with my two best friends. All three of us had iphones, and my best friend switched to an S3. All of our group chats still worked. However, the day I got my S4, only my other friend (with the iphone) still came through on group chat. My friend who had the S3 started coming in individually - on my phone only - my friend with the iphone still received her texts as part of the group! Very confusing. My group chats worked great with everyone else, because I had done some of the steps listed above. I haven't seen my friend in person since I got the S4, but I do believe the problem is her former imessage account. The messages would push through fine as long as I still had an iphone, but now that I don't there's some glitch somewhere - and I think it's because she hasn't followed the proper steps of separating her phone number from her apple ID, especially since her husband still has an iphone with their shared ID, as well as an ipad and a MacBook. These are only theories, and I can post an update once I see her in person (because I have to do this stuff for her - she's not gadget oriented =P).
I just wanted to reassure anyone who was wondering that this is possible, and in fact is as easy to do as it is on the iPhone. Or it's supposed to be as easy, anyway. And as much as I love my S4 (I just wanted to try something different), I am still very much an Apple lover, and have a full apple household (ipod, iMac, iPad, apple TV, husband's iphone 5). However, saying that, for Apple advocating their products as things that "just work", they don't make it very easy to switch to something different. I realize they don't want people to switch, but the point of having something that is supposed to be so easy and user friendly is that it IS easy and user friendly - and going away from imessage sometimes clearly is not. I hope everyone who is having problems can get them sorted out!!
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