Edit
Edit is often overlooked in the "best text editor" stakes; it's not particularly sexy in that it doesn't do context-sensitive colouring like StrongEd or Zap (that is, picking out all the commands in a program or HTML document and making them a different colour to "real" text); it's wordwrap is rudimentary; it doesn't have spell checking capabilities; it doesn't have different modes with button bars along the top to offer shortcuts to save you typing or wading through menus.
However, it has a number of virtues; firstly, it's always around. As it's given away free with your computer, and indeed built into the ROM of most versions of RISC OS 3, even if you hard drive completely breaks you still have a text editor available to help with rebuilding. Another thing people often go back to Edit for is the advanced search and replace function - although most editors have this ability, Edit is the easiest to understand. Although StrongEd now has a widow listing all it's advance search functions it's still hard to use without knowing how regular expressions work (like in the PERL programming language); with Edit's two modes all the functions are written in plain English in front of you.
StrongEd
Originally written by Guttorm Vik, this editor has been shareware, commercial and now freeware, although as Guttorm has now gone over to Linux the future development of this editor is uncertain. It did however spawn the StrongHelp hypertext manual program, which is an invaluable tool for programmers on a budget.
Along with Zap, this is one of the two main contenders for the accolade of "best text editor". Where Zap is better for programming - both have automatic indents and bracket matching, but StrongEd doesn't un-indent when you close a nested programming chunk - StrongEd is nicer to use and has a smaller memory requirement, so it's ideal for non-programmers; although I use it for programming in BASIC and PERL I don't count myself as a "real" programmer. One of the nicest features is being able to select multiple lines and then type in a few characters which appears on every selected line - handy for adding bullet points to every line in a HTML document for instance. I've also been helped many a time by it's internal auto-save - if you accidentally switch off the computer, or crash it, next time you restart StrongEd the document will still be there, usually with the cursor in exactly the same position in the text as you left it.
Zap
Zap has a great advantage of StrongEd in that, at the time of writing, Zap is still being developed and StrongEd isn't. Although both editors have the ability to add new "modes" and resources, Zap has a strong following and plugins are more readily available.
Beyond this, Zap is a strong editor with a technical bent - if you're planning to do any serious programming then this is probably the editor for you, with, for instance, a much better C mode than StrongEd, and other extras like being able to grab areas of memory for examination. Where I feel it loses out is the look and feel - StrongEd is nicer, Zap is more functional, for instance the Zap HTML mode has a small bunch of differently sized icons in a separate window where StrongEd has icons of a regular size in the standard toolbar across the top of the editing window. However, the Zap approach is more compact.
Conclusion
It really depends on what you're going to be doing most of the time; if you're not going to be doing any programming, editing of raw HTML or anything more than just reading the occasional help file, then Edit is perfectly serviceable. If you want to do more complex things in a nice environment, StrongEd is a good starting point. If you're a hardcore coder, then you've probably already made up your mind and have been using Zap for years.