To be honest you've both got a point - you're right that Henry held onto his throne at a difficult time, seeing as how he faced down numerous plots and rebellions which had a chance (however slim) of replacing him, but equally, with hindsight, his rule really was more to the end of the wars, though that's something not necessarily thought by contemporaries. Whatever, it's poetic effect
- don't feed people trying to get a reaction out of you.
Anyway, as for the OP's question - I think it depends on the categories by which you define greatest to be honest. Call it a cop-out if you want, but I think there is no "greatest" monarch, but it's best to look at the highest achievers considering the situation they inherited, the means they had at their disposal, and how secure/stable their legacy was. For me therefore, some of the greatest monarchs we've had, to limit myself to the ones I've learned about, are Edward I (because he managed to conquer Wales essentially and it was quite secure), Henry VII (given the way he managed to secure himself on the throne and start the process of breaking the nobility's power), and Elizabeth I (because she managed to provide some political and religious stability after the relatively poor, and short, rules of her siblings).