I see much more boldness and innovation from the right wing Charedi leaders than from the Modern Orthodox leaders. Major Hashkafek (philosophical) issues that were unresolved in the time of the Rishonim (500-1000 years ago) are suddenly resolved and crystallized. The obligation of a father to teach his son a trade has been suspended in some right wing Charedi circles. Bold speculation in the area of theodicy (how G-d judges man) is more likely to come from the right wing.
On the other hand a Modern Orthodox Rabbi is more likely to wear what many have concluded is Techelet in their Tsisit.