My primary focus for lateral guidance during approaches is the TRK/DTK/XTK figures on the GPS. There is a slight increase in cognitive workload because your brain is having to process the numbers and do the comparisons rather than just visually interpreting a CDI, however, I've found it to be less work overall than the traditional method of only using the HSI and reacting to needle movement. The HSI approach is functional, no question, however in cases where crosswinds change dramatically during an approach (such as 40kt direct xwind at 3000 AGL shearing to 10kt xwind from opposite direction at ground level, thank you Sullivan County, NY, for that little gem a few years ago), DTK/TRK/XTK lets you stay on top of it in real time. Without it, the heading you were flying 20 secs ago is no longer cutting it, and you genuinely have no idea by how much.
So, all things being equal, I've found DTK/TRK/XTK to be a huge win. In known calm conditions, I will sometimes relax for a little while and transition to using the HSI for long periods of time, almost out of guilt and making sure I'm well-versed in both techniques, and to keep an honest tally of which technique is best for me, and under what circumstances.
Granted, on precision approaches, I'll tend towards leaning on the HSI a little more and crosscheck with the GPS figures. That allows me to focus on lateral and vertical on a single instrument. Otherwise, it is, admittedly, a pain in the ass to be parsing the lateral guidance from the GPS while using the HSI for vertical.
I realize how odd all of that might sound, but maintaining 0.00nm, 0.01nm (60ft) or at worst 0.02nm (120ft) lateral deviation during the approach pays dividends at breakout, and, again, removes the enormous pain in the ass of variable crosswinds which would otherwise lead to a needle chasing situation. In short, using the needles only is more of a "oh, we're slowly drifting off course, let's try a correction and see how it goes..." whereas using the GPS is, "these numbers are a little bit of work to read and compare, but BOY do they work fast and with minimal correction."