I’m not aware of evidence that rules out difference in sound between streamer models, but counting on this piece of kit in a music playback chain to make a “next level” difference in sound is a pretty dubious gamble based on how streamers and human hearing work.
I’m also not aware of a streaming service that discloses source info for each track/album it provides; this is not an insignificant detail since a huge number of albums have been remastered. If you are being provided with recent remasters or files that are otherwise likely compressed in dynamic range by your streaming service, then your source files are where the most considerable improvement could be. Either that or equipment to properly process your digital signal specific to your room (DSP), but to get either of those as turnkey would be very expensive.
There are presently no published / accessible studies that demonstrate audible differences between streamer models (vs., e.g., speakers). In buying a streamer, the only surefire thing you pay for = software support and the pleasure of the user interface (touch screen and/or smartphone app), and you hope that the manufacturer keeps up with iOS / Android updates if using a phone app.
I’ve had that very investment (trusting a company to keep the user interface up to date) go bad on me, which is why I now stick with open source for a transport OS. I will not use a streaming service that doesn’t provide source/master metadata for its music catalogue. If you’re unwittingly feeding remastered files of compromised dynamic range into your system, it would a fool’s errand to try to improve things with a fancy streamer.
A good question to ask before trying to take your system to the “next level” is “What do I perceive to still be missing?” based on noteworthy experience(s) from music in your life. Otherwise it can be putting money on the fork with which you stab into the dark ;)