Motorola has mostly used TI OMAP processors in the past from the low-end to the high-end, and also Tegra in their Atrix smartphones and their Xoom tablets. But things are about to change with the new wave of smartphones from Motorola, which apparently will start using Qualcomm's latest and more powerful chip - the dual core 1.5 Ghz S4.
So why the change? First of all, the TI OMAP chip seems to have fallen off the face of the Earth in terms of competition. Ever since they delayed the OMAP 4460 1.5 Ghz which was supposed to arrive last fall, and it only arrived this year in the Archos Turbo tablets. By now they were supposed to ship the dual core 1.8 Ghz OMAP 4470, but no news on that either.
Second, the only other competition for the S4 right now would be Tegra 3, and I don't think Motorola has been extremely pleased with Tegra in the passed. Plus, given a choice I'd choose the S4 chip over Tegra 3, as I believe it to be faster in most real world scenarios, except perhaps in graphics, but the difference is probably not that big right now.
Another competitor would be the Exynos chip, but Samsung probably didn't want to sell it to them when they requested for it. But I do expect to see other companies using Exynos chips in the future. The Meizu phone is rumored to have the same processor the Galaxy S 3 will have, but it will be launched around 2 months later. But what makes it interesting is the Exynos 5250 chip based on Cortex A15 that will arrive later this year, and will probably be the most powerful chip in the market then. I'd really like to see that chip in devices other than Samsung's phones and tablets, as well.
For now, though, Motorola made a good choice using the S4 for their upcoming devices, but I hope they try to get that Exynos 5250 from Samsung as soon as they can.