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I haven't tried Alexandria to Cairo by train - but did take the Cairo to Luxor overnight train two years ago - cost was around £60 return for a sleeper cabin - trip took around 10/12 hours each way - certainly not at 130MPH.
The bus ride from Alexandria to Cairo was, expensive, noisy and generally uncomfortable - plus you are locked in to the tour schedule. Doing your own thing is more pleasant - except that you still may find yourself fighting to get in to see the Pyramids - as everyone and his dog will be going there from the ship also. The other thing to keep in mind is that once you do elect to go it on your own you will find yourself at the mercy of the locals - you will do well to check prices for taxis and for entry to see close ups of the Sphinx and Pyramids. Ripping off the tourists is a well practiced art in Egypt and extremely difficult to avoid.
However - as prices there are generally very low anyway paying even massively over the odds won't be so bad.
The organised tour also takes in the Cairo Museum includes the entry fee - but not the additional fee of around £10 pounds sterling for access to the royal mummy display - this is well worth a visit.
Finally - the tour to Cairo organised by Cunard is a 12 hour round trip - if your ship is staying overnight at Alexandria then you have the opportunity of staying over in Cairo. The cheap and very characterful Windsor Hotel is basic but adequate for a stopover and at around $30 US per night quite a good deal - plus they have a great bar!
The Hotel also arranges trips to the various sites and their experienced driver can save you time and stress - you can then plan to go when the crowds have gone possibly early morning or late afternoon - even at night to see the Pyramids spectacular floodlight didplay - make sure you negotiate a reasonable fee and promise a tip.
We travelled from Alex to cairo in Nov by train, just turning up at the station - not a good idea, because the turbo train at 8am was fully booked. had to take the 10.10 which arrived in cairo at 1pm not leaving much time for visits in/around Cairo. You need to pre- book the tickets - Egypt trains have a website. It was £9(UK) 1st class return. came back on 6pm turbo -45mins late leaving Cairo leaving us 15 mins to get back to the ship - exciting but a little stressful. definitely better than the coach convoy we heard about from fellow travellers. Cairo Metro v. good. Get off at Cairo University or Giza and then a taxi to the pyramids.(£50 Egyptian - £5 UK). Be prepared for VERY primitive toilet facilities all the way!!