Well....again this may well be a fairly deep discussion, particularly when just getting started, but we'll start with the general broad brush stroke notion of the absolute enormity of importance the idea of unity gain and proper gain staging. That is to say where to adjust gain as opposed to where to adjust volume and how it may cascade into various problems. Remember once we're talking about digital overs there's no fixing it in the mix. An over is an over for eternity.
I am also a firm believer in the cleanest audio comes from the simplest input structures. When you choose to run through a mixer (with its input gain structure, its channel gain output, its active eq and finally its master gain output) then further the path into yet another analog gain stage (in the Presonus) the idea of unity gain and controlling levels (and noise) becomes more complex and certainly opens avenue for problems. It can be done and it can be done properly but it requires a bit more setup and monitoring.
Finally (for now) I'd submit comparing a new audio system (your Presonus) to a tried and true listening environment (your board and headphones) can often at first listen seem massively different. Most likely because of different input and output structures. I'm bettin' my bottom dollar the Presonus is capBle of "as clean" or more so monitoring as your board.
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