The 'like' operator indeed exists since 3.6, but the eztext and ezxmltext datatypes unfortunately don't support attribute filtering.
There wouldn't be a problem to implement it if the content of the datatypes contains less than 256 characters. In case there are more characters, some truncating is needed which is kind of pointless for those datatypes (the database field for string attribute filtering is a VARCHAR(255) in mysql and pgsql).
I think it's possible to implement what you want using extended attribute filtering. Just do an sql LIKE operation on the data_text field for the datatypes.
Yes, it works like a charm for text line but I was wondering about the two "long string" types, mostly.
I'll likely write an extended attribute filter some time (or maybe see if I can hack the core and submit it as patch), but for the time being, I'll likely be able to get away without it ;)