Ooh, that's a difficult choice.
For three days in Cairo/Giza, I would pick:
- Day 1: Pyramids and the Grand Egyptian Museum
- Day 2: Saqqara and Dashur
- Day 3: Cairo (citadel, mosques, souks, etc). I didn't sail on the Nile in Cairo, but I think that some possibilities may exist.
For three days in Luxor, I would pick:
* Day 1: Valley of the Kings and the west bank
* Day 2: Luxor east bank (Karnak and Luxor temples)
* Day 3: Abydos and Dendera
I would lean slightly toward Cairo for the following reasons:
1) Pyramids at Giza. It's hard to imagine going to Egypt and not seeing the pyramids. Admittedly, you only need to see them once --- we skipped them on our second visit to Egypt -- but I am so glad that I saw them. If you are in reasonable physical condition, I highly recommend going inside the Khufu pyramid. I just have to pinch myself every time I look at the grainy, dark picture of me standing at the Khufu sarcophagus.
2) I have only been to the downtown museum, but, wow. Just wow! I can only image what the GEM will be like.
3) Saqqara and Dashur give a good perspective on the rise and fall of the Old Kingdom, with a little dose of the New Kingdom thrown in. I learned a lot more at Saqqara/Dashur than at Giza. It's fascinating to look at the progression, of pyramids in particular, from Djoser to Sneferu to Khufu and then to see how things deteriorated by the end of the Old Kingdom.
4) Cairo - Very different from any city I have ever visited, including Amman.
Luxor, on the other hand, is the place to go if you want to explore the New Kingdom, most notably the Valley of the Kings and the east bank temples. Abydos, one of the oldest sacred sites in Egypt, is historically very significant, but not especially pretty to look at. Dendera is not as historically significant, but really beautiful. You will have plenty of opportunities for short felucca cruises on the Nile in Luxor.
You really can't go wrong either way.