Does one use more battery and data then the other?
They probably use about the same amount of battery.
As for data: plain SMS messages do not count as "data" when it comes down to billing by the cell carriers. SMS is seen as a separate thing altogether. If you're on an "unlimited" texting plan, then the text message has already been "paid for" in your plan, and doesn't count against anything.
Of course, if you have NO SMS plan, then a text will incur a usage charge (usually $.20-$.25 per text), even if you have available data usage remaining in your billing cycle.
Push notifications can also go over wifi and other internet connections. So, if your phone happens to be connected over wifi, then your cell carrier won't see or bill for the push notification at all: it won't count against your texts, nor will it count against cellular data.
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Is one better then the other ?
Depends on what you're looking for. If you don't want to use any of your data at all, and you have unlimited texting anyway, then SMS is the way to go.
If however, you want the ability to receive notifications over WiFi, even if you don't have a cell signal, then you want to go with a push notification
Also, push notifications let you receive the message over more than one device. If you also have an iPad, iPod Touch, additional iPhones, or a Mac, then you can also get the notification on all of those devices too. Can't do that with SMS.