Sure, a PDA has more computing power by a few orders of magnitude than those Apollo era computers. There are some other systems, primarily avionics, that are also considerably smaller and lighter today than in the 1960s. For example, the inertial navigation system for a modern spacecraft would almost certainly use laser ring gyros that are much smaller, lighter, and more accurate than those earlier units. However, avionics weight was only a small percentage of the Apollo CM or LM vehicle weight.

There has also been some improvement in materials that could allow for lower structural weight, perhaps by several percent. These savings would probably amount to a greater weight reduction than the improvements in avionics technology. I don't know how much more we could reduce the Lunar Module's weight since Grumman spent years shaving every possible ounce of excess weight during the vehicle development. Newer materials might cut some weight but I doubt it would be substancial, at least for the LM.

For some of the other systems, there really wouldn't be much weight reduction at all. People still breathe the same amount of oxygen, eat about the same amount of food, and drink the same amount of water each day now as they did then. If anything, most people probably weight more today (on average) than then. Perhaps the best reduction would be a crew of midgets or petite women, but that would really go against the public image of astronauts.

For at least the first missions, you'd almost certainly still be using hypergolic propellants. That alone would constitute a huge percentage of the total vehicle weight. Isp for hypergolic engines has not improved very much if any since the Apollo era. If accessible ice does exist on the moon as we all hope, then eventually we might be able to set up processing facilities and switch to cyrogenic propellants like LH/LOX. That would represent a huge increase in propellant efficiency (almost 50%) allowing for a much greater payload.