I think I would be right in saying that Androids biggest equivalent is WhatsApp (although there are others), which of course is on iOS as well. If I know a person doesn't have data I'll use SMS, but I like that with What's app you can see the message is sent (one grey tick), delivered (two grey ticks) and read is two blue ticks, it works slightly differently for group messages. You can send pictures without the risk/cost and poor user experience of mms.
Of course issues still happen, the recipient might read it on the lock screen or notification bar, so it doesn't show as read, they may even reply to the wrong person, something I've done a number of times. Read message in notification bar, then open app, which is in a different conversation - must remember to use reply.
The best thing with WhatsApp is its cross platform availability. I use a lot now to communicate with customers, in a lot of circumstances it's easier and more convenient for both parties than email.
Actually it's just occurred to me that the Android direct equivalent to iMessage is
Google Hangouts which combines instant messaging, video chat, SMS and VOIP features into one App which is the very reason I've never used it.