When comparing iMessage vs GroupMe, the Slant community recommends iMessage for most people. In the question“What are the best messaging apps for iOS?” iMessage is ranked 5th while GroupMe is ranked 21st.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Secure end-to-end encryption
Pro Cross-platform within Apple ecosystem
iMessage is available on iPhone, iPod, iPad, and Mac.
Pro Supports voice messages
Short voice recordings/messages can be quickly sent, and messages can be easily dictated into written messages as well.
Pro Free and unlimited messages over Wi-Fi and data
Messages clearly indicates whether messages are being sent over iMessage (blue) or SMS (green) where messaging rates apply. iMessages do not count as SMS messages with your carrier, instead they use a negligible amount of data to send over Wi-Fi and cellular data networks.
Pro Clear indicators for message delivery and receipt
The app indicates when messages have been sent, when they have been read, and when someone is typing.
Pro Comes pre-installed
No need to download or sign up for a new service.
Pro Seamlesss switching between SMS messages
Pro Friends don't need to "sign up"
You can just message them using their existing phone number or Apple ID and they will get your message.

Pro Clean UI
UI is minimalistic, and clear. And there is a plethora of stuff on the left of text box if you wanna use them.
Pro Apps and games for iMessage are available
For example, you can play games like pool or you can show someone a destination to go to.

Pro Reads receipts
GroupMe has a built in function to read receipts.

Pro Great web client
GroupMe has an excellent web client that can be used to send and receive messages and manage groups from the desktop.

Pro IFTTT Integration
Allows sending messages from web services via IFTTT.

Pro Integrated calendar
It's possible to add location and time with reminders directly in the GroupMe app.

Pro Makes it easy to silence 1 or all groups
GroupMe has settings that allow muting a single group or turn off all GroupMe notifications from within the app.

Pro Does not require everyone in the group to have a smartphone
GroupMe can set up a custom phone number which allows people without the App to send and receive messages. This makes it easy to add anyone to messaging.
Cons

Con Not cross-platform
iMessage is not available on anything but Apple devices.
Con Can't send separate texts to individuals who share a Contact record
iMessage is an utter disaster. It can't send separate texts to anyone who is on a shared Contact record but with separate mobile phone numbers (e.g., "Paul and Angie Smith"). It merges ALL threads that ever went to ANYONE on that shared Contact record. Want to text just the husband to set up a surprise party for the wife? Not possible. iMessage will ONLY add that new text to the EXISTING thread you had with the wife. Duh! iMessage is pitifully incompetent.
Con Blocking Spam Messages takes 3 steps more than is needed
You have to open the message, select the sender, open info on the sender, then block sender. The default Android message app, select the message, block sender. it automatically deletes the message and blocks the sender.
Con iCloud sync of message is not stable
Sometimes, the messages on different devices with the same ID will be different, the syncing function work poorly.
Con Slow and unreliable
Con Drains battery fast
GroupMe, in order to have a constant connection which allows for notifications drains the battery of a device quickly, which is not ideal for a messaging app that one needs on time notifications from.
