Apple TV Streaming Sound Quality vs Streamer?

I am looking for the weak link to improve sound quality.   Seems logical it is the Apple TV as a source.  Would a moderate streamer inside of $1500 make much of a difference when streaming Tidal and the like?  

Current Equipment:
Speaker: Dali Euphonia MS-4
AMP: Modwright KWA 150 SE
Preamp/ DAC: Peachtree Grand Integrated
Source: Tidal / Apple TV
I would say yes. 

ATV does not support 24 bit streams and resamples everything to 48 khz so it is not a "bit perfect" device. This in itself doesn't mean that it doesn't sound good, but it leaves room for improvement especially considering your paying for Tidal. Additionally you can improve general usability by getting into a prettier and more robust streaming GUI. 

The BlueSound Node or Auralic Aries Mini would be good places to start looking and both are under $500. Alternatively, you could swap out your Peachtree integrated amp for a true preamp that incorporates this type of functionality. This could further improve usability by folding proper volume control into the same app.  

If you are committed to going further upmarket, You could take a look at Roon as a front end. This would allow you to use a network audio adapter like a sonore microrendu or SotM device. Even the BlueSound and Auralic gear would  allow for this. Roon opens the door to a world of cool functionality and nearly infinite flexibility. 

It really depends on what you want to do and your predisposition for tinkering and upgrading. You have some very nice gear. 

I would dip your toe in the water and have fun with it. Streaming is the best thing to happen to high end audio in years. 

Robr45 makes some good points.

The Apple TV is a great device and can sound wonderful when connected to a well designed system, but because of how it samples/clocks, a dedicated AirPlay source/stream can sound better when properly implemented.

I mention AirPlay because it’s a high quality (bit perfect) transport/network source that is integrated into all of Apple’s operating systems and applications.  You can use Tidel directly into a nice AirPlay/DAC if you use Apple Mac or iOS (iPhone/iPad).

If you move away from the Apple TV interface, how would you prefer to control your music?
Sorry if this a bit off topic, but out of curiosity, how do you stream Tidal through the Apple TV box and what connection and how do you mange/view the Tidal music content?