Tell the neighbour to go suck a lemon.
Usually a minimum of 2 quotes are required to validate you are not getting ripped off by the owners mate. 3 quotes being the usual norm.
I'd call you local governement building section and ask them what the rules and regulations are in your area. If there is an existing undamaged fence already there, you do not have to do anything.
The owner of the other property can install a new fence at their cost. You do not have to pay half.
I'm assuming they have put up Colourbond fences on the other sides of their property and want to change your fence to suit. You do not have to agree to this, nor pay for anything. In some cases I have seen people erect a colourbond fence next to the Hardie fence. (i.e. they lose a couple of inches of their property, but it is all nice for them and you retain the same look in your property)
If they want to have a survey done to re-peg the fence lines, that is all at their cost. I've had a neighbour do this once and they ended up losing property and I got to chuckle a lot
Long story short, they have issued you a letter with a timeframe on it to try and pressure you into the decision. This means crap all in my opinion and only makes unnecessary tensions between neighbours. Go talk to you local government's building section as they will point you in the right direction. Most likely after this you can then send them a letter back telling them where to stick it and for them to reply in 21 days