I don't know. If they are sms messages, they should be delivered in the same manner as the 4S. If you're referring to iMessages, if the recipient does not have an iOS device AND you do not have the "Send as SMS" option enabled on the iPhone 4 then that could prevent them from receiving your messages. Furthermore, it could be a network issue. Try going to Settings-General-Reset and then select "Reset Network Settings" on the iPhone 4.