Would you be willing to elaborate a bit on the differences between the Manhattan and the RME? I have an RME and am happy with it for my preferred application (cough cough, internet radio) but I imagine that Tidal could sound a bit more refined. Thanks!
Using the line out (XLR), both are excellent when it comes to detail, with the RME sounding a little lighter than the Manhattan. The RME sounds a little hard (relatively speaking!) in the mid and seems to present less of the natural warmth in acoustic instruments and voices than the Manhattan. Here goes the subjective! The Manhattan seems to put me in the concert hall or at the gig and preserve the atmosphere and emotion of the performance more effectively than the RME. Basically, I forget the HiFi and get lost in the music from the first note with the Manhattan, whereas I sometimes end up analysing the HiFi with the RME. It's a small difference though and could be system/room dependant.
One of the main differences in how these DACs are constructed is in their power supplies and analogue circuitry. The RME has a single switch mode supply and simple stepped analogue attenuation levels intended to mitigate any down side associated with the digital volume control it employs. The Manhattan includes two separate linear power supplies, one for the analogue side and the other for the digital. It includes a good analogue preamp section (which, to my ears, equals or beats some well respected alternatives) with a fully analogue volume control (which I prefer to the digital control that can be used as an alternative) that I use all the time.
You mentioned Tidal. I have it but don't use it much because of its heavy reliance on MQA, which I don't like. The Manhattan can fully decode MQA, but I find the sound to be artificial (not just on the Manhattan). If you turn the MQA decoder off, Tidal then feeds you a degraded 16/44 file of less than CD quality. The RME does not decode (unfold) MQA. Qobuz (16/44 and higher) is far better on both DACs and is my default streaming service.
On the other hand, to my ears, the RME is the better headphone amp (that is its main use for me). Its sophisticated DSP features are very helpful in this application, as they allow you to fine tune the frequency response on the individual channels to compensate for differences between your ears and to tame any peaks in your headphones' respond curve very effectively.
Hope this (sorry rather long!) post helps!