The measure of success is not whether you have a tough problem to deal with, but whether its the same problem you had last year. (John Foster Dulles)
We mainly deal with the four systems listed - but there are many others available to businesses. Some are based on particular applications (e.g. a workshop), and some are based on products from various sources.
We will consider almost anything, but the final decision will depend on how well the program suits NZ accounting needs. For example, we would not be keen on working with a program that required GST rates / amounts to be entered manually on every transaction, but if it required some work to cater for a change in rates, then we could accept that.
However, we generally do not accept cash-books. People who want to work that way have the choice of using a bank feed - which really reduces the amount of work, but generally cash-books can leave a lot of gaps. A normal accounting system will make it much easier to reconcile debtors and creditors. If you really want to use a cash-book there are many accountant's around who will provide the services your want.
Having said that, we were advised that one of the major cash-books in NZ actually has a full GL version - something I was previously unaware of. I have in the past supported Accomplish cash-book clients. While I have said I am not going to support clients who choose to stay with a cash-book, they do have a full GL (but not including stock) version available.