R6RS has syntax-case macros which is superior to Common Lisp macros in every respect, they're both hygienic and can be used to implement a sloppy macro system if one so wishes.
`syntax-rules` is very good and you can do a whole lot with them. However, you are limited to template -> pattern transformations, and there are plenty of macros that you cannot write this way. (E.g. anything requiring a predicate on the source syntax that you can't express in the template language, etc.) For that, you need the full power of procedural macros.
My mistake: R6RS has `syntax-rules`, not `syntax-case` as far as I can tell. However, `syntax-rules` and `syntax-case` are equivalent in power. [1]
It does not have the same power as `defmacro`: you cannot define general procedural macros with `syntax-rules`, as you are limited to the pattern-matching language to compute over and construct syntax objects.
I think you got your wires crossed. R5 and R7 only have `syntax-rules` macros. R6 has both (`syntax-rule` can be trivially defined as a `syntax-case` macro).
R6 having `syntax-case` macros is one of the more controversial things about it; a surprising number of implementers don't care for them.