In terms of outer iterations, SQP should win because it includes second derivative information, whereas augmented lagrangian methods such as ADMM do not.
However, one thing to keep in mind is that each iteration for these methods involves solving a linear system, so to do a fair comparison you have to take into account how easy these systems are to solve.
For augmented lagrangian (alternating) methods, each iteration you are solving something like,
$$(A^TA + \rho I)x = b,$$
where $A$ is a forward operator straight from the objective function that is known and usually easier to deal with or precondition, and $\rho$ is the penalty parameter. (eg, your problem is $\min_x ||Ax-b||^2$ subject to some regularization and constraints).
For SQP methods you are solving something like
$$Hx = g,$$
where $H$ is the Hessian (or approximation thereof) which is usually only available implicitly in terms of it's action on vectors, and $g$ is the gradient. The Hessian contains not just $A$, but also a combination of other matrices and matrix inverses coming from linearizing the constraints and regularization.
Preconditioning Hessians is a pretty tricky business and is much less studied than preconditioning forward problems. A standard method is to approximate the Hessian inverse with L-BFGS, but this is of limited effectiveness when the Hessian inverse is high-rank. Another popular method is to approximate the Hessian as a sum of a low-rank matrix plus an easy to invert matrix, but this also has limited effectiveness for hard problems. Other popular Hessian estimation techniques are based on sparse approximations, but continuum problems often have Hessians that have poor sparse approximations.