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When a customer switched phones in June, if they had an Android(s GOOG) or an iOS(s AAPL) device, they mostly stayed committed to that OS. But, according to Consumer Intelligence Research Partners’ latest research, iOS users in general were just a bit more likely to stick with the iPhone than and Android users were to pick another Android smartphone.

Here’s CIRP’s chart calculating the loyalty rates of smartphone users by the mobile OS they choose. It shows 78 percent of iOS users chose another iPhone, while 67 percent of Android users stayed with Google’s OS. There is some switching among those though: 14 percent of former iOS users went Android, while 27 percent of former Android users crossed over to the Apple mobile ecosystem.

You can also see how iOS and Android are continuing to decimate the previous era’s smartphone champ, Blackberry(S BBRY): 34 percent of former Blackberry users switched to Android, while nearly half, 48 percent, moved over to iOS.

But the real battle that that Google and Apple need to focus on now is winning the feature phone users who have yet to upgrade to a smartphone. So far, Android is winning, gathering 50 percent of basic phone users, while just 39 percent chose iOS. This fight explains why Apple is pushing its iPhone 4 and 4S so heavily (and having pretty good success). It wants to lure in users who don’t mind upgrading to a fancier phone as long as it’s cheap, like the free iPhone 4 or $99 iPhone 4S with carrier contract.

In this chart, you can see a more granular break down of Android device makers and how their individual loyalty rates compare to the iPhone:

Just as the previous graph showed, iPhone owners are pretty loyal, with a 78 percent retention rate — though if they are going to switch, they mostly end up choosing a Samsung device, which speaks to Samsung’s aggressive recent ad campaigns against the iPhone. Samsung performs next best, with 52 percent loyalty to its brand of smartphone. But HTC (27 percent), LG (18 percent), Motorola (9 percent) and Blackberry (10 percent) performed miserably when it came to keeping their customers.