The filters are clearly a significant part of the process and one reason DACs sound different. This is particularly true for DSD. That is why most comparisons of PCM and DSD are flawed. What you are really listening to is the particular DAC's implementation of PCM or DSD conversion to analog, including the filtering, rather than any inherit difference in the formats. Even DAC's that implement both, use different filters for the two different formats. And some DSD DACs convert DSD to PCM internally, without telling you. So, the real question comes down to how your particular DAC implements PCM and DSD and how that sounds to you. I know that sounds trite, but it really is true in this case. Two people can listen to the exact same comparison and hear different things. That is the wonder, and the frustration, of human hearing.
One reason to go to higher resolutions is in order to minimize the effects on the filters. At 16/44 or 2.8 you need a pretty steep filter to keep noise out of the audio range. The higher the resolution, the less steep the filter needs to be and the less filter anomalies enter into the normal audio range. With DSD 5.6MHz, DACs can move down from 5th or 7th order for 2.8 MHz to 5th or even 3rd order filters, which can mean significant difference in filter anomalies. Again, which filter to use is up to the DAC designer.
People often scoff at the idea of these higher resolutions because people cannot hear above 20 KHz and most cannot hear that. However, the higher resolutions do move noise higher up into the spectrum which can clean up the normal audio band. In addition, there is certainly evidence that the brain, which is ultimately the processor for sound, does recognize subtle differences due to frequencies higher than 20 KHz, even though we cannot hear them as a sustained tone.
I had the chance to talk to a well know speaker designer recently and I asked him what he thought about having speakers that went above 20 KHz. He talked in depth about one of his most recent designs. He originally put a 20 KHz tweeter in it and it just did not sound right to him. So he put in a 40 KHz tweeter (they design their own tweeters) and it sounded much better. He ascribed the difference to the harmonics that were being generated by the two designs, similar to the observations in the article that ferday linked to.
Some DAC have the option to choose between multiple filters. I sometimes think it would be interesting to have the DAC do no filtering and have a "filter box" in line between the DAC and the pre-amp that would allow the user to dial up different filters and listen to the difference. Even order, odd order, steep, gradual, even different types of filter algorithms. I think it would show that the filters can have a significant effect on the final sound. It would be particular interesting for DSD. No practical, but something to think about.
In the end, it depends on the DAC implementation and how it sounds to you. Trite, but as true for DACs as for any other component.