You're correct, without inequalities, the interior point algorithm is a fairly straightforward algorithm. In the case where your problem only has equalities, the trust-region-reflective algorithm can be advantageous. Note, however, that you must provide analytical derivatives in order to use it.
The interior-point algorithm implementation has other features that add robustness: e.g. Hessian approximation options, ability to effectively use sparsity in the problem, ability to work with ultra-large problems via CG solves, etc. Therefore, it's usually worth trying as a first step.
