To be honest, all consultants are very busy, and I don´t think partner is the worst tenure.
This said, partners are really busy people who devote many many time to the company. Furthremore, since they have several engagements at the same time in different parts of the globe, they travel a lot, which makes it heavier.
However, i believe that Engagement Managers or Junior partners even have a harder time and worse work-life balance, since htey have the carrot hanging just in front of their faces.
Hope it helps!