The problem is that an upgraded DAC won't do a thing for your small room, low power setup. You are buying reference level gear for a non-reference level setup. Basically throwing money into the wind. It's great that you have some expendable cash flow, but it simply makes zero sense to spend it where you are looking to spend it at the moment.
The DAC inside your streaming device is good. It's not as nice as what you are looking at buying, but it comes down to whether or not you will get any audible difference based upon the equipment you have. Generally speaking, you simply won't. You aren't listening at the levels you would need to get a real difference. A very subtle difference? I would expect so, yes. But, you can get a wildly superior jump in audio quality simply by filling in the areas which your system is currently completely lacking as pointed out previously.
Both DACs are perfectly fine. They will likely make a very subtle improvement to any system. Subtle being the key concept. Anyone claiming 'night and day' improvements is just lying, or is starting with garbage and noise as reference.
You are past the first 90% in terms of DAC quality, and you are not anywhere near 90% in terms of speaker and room quality. That's the first place to improve your audio.
After that, if you still want to spend money, you would need to try both DACs and see which one manipulates the audio in the way that you find most enjoyable within your system, with your specific gear and you need to consider if the subtle upgrade you are spending a lot of money on actually was worth it. Which is not something anyone here really can decide for you. Kind of like the Camaro/Mustang argument. On paper they have a lot going for both of them, so which one is better? The one you LIKE is the better one, no matter what it says on paper. But, neither are a Corvette, or a Porsche, and it doesn't matter for any of them since you can't drive them 100mph+ and are stuck in rush hour traffic. The first step is to get out of that traffic and allow reference level testing with proper reference level gear. That's the big hold up to your system's quality right now.