I felt similarly after moving from vBulletin and was met with the answer "moderator actions/tools should be sufficient" when I searched around. I devised my own little solution, though -- making your moderators administrators of a sort. When you add a new administrator through the Admin CP, you can set what exactly they can do through the ACP. A lot of add-ons will add permissions here which is really useful.
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I give my global moderators
manage threads and posts, manage attached files, manage infractions, and
manage bans. That seems to parallel the vBulletin Mod CP to me, with the exception of things like editing signatures and avatars, but there are add-ons available to allow that.