If your digital sounds less fleshed out and natural. Then it is the components... streamer and DAC that are the reason. These days it isn't the source medium but the components that determine the ultimate sound. So, I would first look at getting a warmer more natural sounding DAC. If that doesn't pull ahead your digital leg, then upgrade your streamer.
I have extremely good analog and digital ends, both of which are detailed, natural and musical. I can switch back and forth and not tell which is which... or do that for a friend and they cannot tell.