The biggest difference is that Topaz Labs is an offline software that you install on your computer, while TensorPix can be used through web browser.
Because Topaz runs on your PC, it uses your hardware to process files. This becomes problematic if your PC isn't quite high-end (and most users don't have high-end computers). You can still use Topaz with a less powerful computer, but the processing speed will be heavily impaired, meaning you could wait for tens of hours for enhancing a mere couple of seconds of video.
On the other side, TensorPix sends all processing to cloud which has access to powerful GPU hardware. This way, every TensorPix user has access to high-end hardware and doesn't have to worry about their computer being too slow.
Using cloud resources has another benefit. Cloud resources can be easily scaled meaning you can process multiple videos/images at once, without worrying if your computer can handle it. You can't do that with Topaz as processing ONE video or image will utilize nearly 100% of your computer’s processing power.