Choose a statement review if you suspect there is something you have forgotten, if you have changed cards or banks in the last year, or if you would rather not give any third party read access to your spending. It starts from ground truth instead of from memory or from whatever a single connected account can see.
Choose a bank-linked app if discovery is the part you dread and you are comfortable connecting accounts. Rocket Money, Monarch Money, PocketGuard and Hiatus all work this way, and the real differences between them are what happens after discovery: cancellation help, bill negotiation, or full budgeting. Connect every card and account you actually pay from, or the picture stays partial.
Choose a manual or guided tool if privacy is the binding constraint, or if you have already done discovery once and now need the list to stay current. Bobby is the minimal version of this; Gravity is the paid iPhone version that adds renewal and trial tracking plus official-source-verified, step-by-step cancellation instructions for each service, which you carry out yourself. Neither connects to an account, so both depend on you entering what you pay for.
Most people end up combining two: one statement pass to find everything, then a tracker so it does not drift back. The order matters — a tracker you fill in from memory inherits exactly the gaps you were trying to find.