Either can work well.. A series of rooms connected by an underlying theme that ties them all together, i.e your idea for a "Saw" type maze can be great, especially if your haunt has a "back story" that can explain why everything is where it is.
Equally as effective can be a series of rooms with different themes, each one playing on individual fears or phobias. A claustrophobic room, a totally pitch black room.. A rat room, spider room, clown room.. the list is as endless as your dark and twisted imagination.
If this is your first walkthrough maze haunt, you might want to go with the individual rooms, see what gets the most reaction and develop it from there, maybe creating a back story that would enable you to expand that particular theme next year.
Personally I work to one constant back story and change up the theme to a greater or lesser extent each year but that is something that has developed over the ten years or so of running our haunt.
Just some suggestions from an "old spook"...I'm sure whatever you decide to do will be a big success in your neighbourhood.. People here in the UK are so surprised to see anything at all that they'll love you even if you dress in a white sheet and go "Boo!".
