When turning the leds on and off, how fast did it react?
I have tried both Electric Imp and Spark Core for my small IoT projects, and I ended up using the Electric Imp for all my things. The Electric Imp both got code running on the device, and on their server, so if you want to pull data down from a API, or even extract something out of a big website, you can have the Agent running on their server do it, and only transfer the stuff you want to the device. Only thing I don't like about it is how sensitive it is to Error40's. If you connect something to it wrong, you have a very big chance of breaking it compared to an arduino. But reaction time from you access the url associated with your Electric Imp, until it responds, is very fast.
But back to the TI, did you measure how much current it draw while running?