... In the grand scheme of things how strong is the white council ...
Nobody really knows.
I presume they've done some pretty epic ass-kicking, in days of yore; they did
something to earn their rep, and the immortals will have long memories, so it's not likely that exaggeration over time will have been a substantive part of that rep.
I think it remains to be seen how formidable they remain; the modern White Council may be a bit of a Paper Tiger. A few formidable members, like Eb & most of the Senior Council, many of the Wardens, a few others... But (particularly with the influx of very-young & inexperienced Wardens) the overall combat fitness of the WC is surely reduced in the post-VampWar era! Certainly there are many WC wizards who are little to no use in combat, nor even much use for logistics/support.