Thanks so much for the reply!!
So if it can take 9-10 or even more months to get the EEA family permits, if we were to not be able to move right as the permits came in and they are only for 6 months
No, it takes a few days to get the EEA family permits. Current processing times for them in Sweden are 41% processed in 5 working days and 83% processed in 15 working days.
So, you would want to apply for the family permits a few weeks before you are ready to move.
and the EEA residence cards can take a few months to come through, what happens if the 6 month permits expire before the 5 year ones come in? Or even worse, is it possible to be approved of the 6 month permit but then denied the 5 year cards? And when the 5 year cards expire, what happens? Do we apply for another 5 year card?
It doesn't matter if the 6-month permits expire before the 5-year residence cards are processed... your immigration status is 'put on hold' so to speak while you are waiting for the visa - as long as you apply before the 6 months are up, the EEA permits will stay 'valid' until you get the residence cards.
I've never heard of anyone being denied a 5 year card after getting the family permit, unless they didn't provide the documents that are required (such as proof of marriage, proof of exercising treaty rights etc.). However, it is really just a confirmation of your right to live here and in fact, it is not even a requirement to apply for one... unfortunately though if you don't you may have trouble proving you have the right to live here for employment etc. and also every time you left the UK you would have to apply for a new EEA family permit to be able to re-enter again!
After 5 years in the UK, you will become UK permanent residents, so you won't need to apply for another 5-year card - you would just need to apply for confirmation of permanent residence (although again, this is not a definite requirement).
I've been looking through the information on the UK Border Agency website, do you happen to know of other links for useful information regarding this?
The UKBA website contains all the official information, whereas other websites are often not accurate as they are not official, so I would only recommend the UKBA website. See:
http://www.ukba.homeoffice.gov.uk/eucitizens/I'm not sure I understand why it would be easier and cheaper to be family of an EU citizen...? Not that I'm complaining but just wondered the logistics of it. Is it simply because it's what is stated in the treaty? Is it more difficult and more expensive if it's a UK citizen's family? 
It's kind of stupid really - family members of EU citizens get more rights in the UK than family members of UK citizens (they can claim benefits right away as well) - plus the visas are free! It's something to do with the EU/EEA laws - similarly, UK citizens can move to other EU countries with their non-EU spouses pretty easily as well.
The only drawback that I can see for the EEA path is that it takes 5 years to get permanent residence and 6 years to UK citizenship, compared with 2 years to permanent residence and 3 years to UK citizenship for family members of UK citizens.... however, the government are proposing to increase this to 5 years to permanent residence for UK spousal visa holders from April 2012 anyway.