I started off with a Pilot III, moved to the Skymap II because I thought the larger screen would be better and now have a GNS430 fitted in the aircraft. My personal opinion of those two handhelds is that the Pilot III is the better of the two simply because it is so much easier to use in the cockpit, not requiring an external antenna for example which I find causes a bit of wire congestion in the cockpit. The one thing I like though about the Skymap is the 'position' field which gives you something you can simply read out when reporting a position ("4 miles NW of Exeter"). The GNS430 is excellent, though obviously stuck to the aircraft! One of the disadvantages of that is that you can't set it up at home beforehand. However once in the air, and coupled with the autopilot it significantly reduces workload.
I still plan most flights with the chart and work out headings and speeds based on the forecast wind (unless I'm just following the coast for example) and I then keep the chart on my lap so I can check where I am as I go. I can't see how this possibly reduces situational awareness though. I always know where I am but do not have to keep looking for roads and railway lines to check! I even get time to get the odd fix with the VOR and DME to check that they are working properly in case the GPS packs up!! :-) The other really great thing is that you can plan a flight fairly close to controlled airspace and be sure you do not infringe it. Quite a few routes from where I am based clip the edge of either the LTMA or the Solent zone and I can now quite happily plan a route that goes right to the very edge without having to plan a detour around in case my DR doesn't work out (EGHR-EGMD for example goes right past the bottom corner of the TMA at anything above 3500 feet and prior to the GPS meant I would always route via SFD to avoid the issue).