Comparison of “Where Is This Used” And “Metadata Search App”
Metadata Search App
Where Is This Used” Button
The Metadata Search App is for developers and admins installed in their org and can be navigated by the tabs.
The “Where Is This Used” Button is situated on custom fields, classes, pages, and triggers in Setup (beta in Sandboxes).  
When you open the app, a panel appears with a search bar and options of components where the search is to be conducted.
When you click it, a new panel appears with a record of the center metadata kinds and a field. 
The logic behind this app is to display a record of the metadata kinds and a field in PDF format or CSV format which can be downloaded and also can send to the user by using the email send button.
The logic behind this is being published as the Dependency API, therefore the method of attempting to delete a field to reveal its usage is employed here.
The Metadata Search App interacts with Quick Search Audit Trials, Approval Processes, Layouts, Flows, Workflows, Validations, Fields, Objects, Reports, Dashboards, Custom Settings, Apps, Roles, Profiles, Groups, Queues, Sites, RecordTypes, Links, Classes, Triggers, Pages, LWCs, etc.
The “Where is this used” button only interacts with custom fields, VF pages, Apex classes, and Triggers and does not look at all metadata items
Metadata Search App gives us the option to type the resource on the search bar and choose the components where we want the search to be conducted and it displays the metadata record list on the page without navigating you to another page.
The “Where is this used” Button is established after going on the particular custom field and selecting to know the related metadata records.
The Metadata Search App is capable to look at a wide variety of metadata types, and so offers a more in-depth examination than the Where Used button.
To look at the wide variety of metadata types and records in the “Where is this Used" button, the developers will need to write some code.
Metadata Search App is capable to show or report on the examination in a more suitable format like in PDF format or CSV format which can be downloaded 
The “Where is this Used" button only displays the record metadata items.
The Metadata Search App utilizes the Search and Tooling API to lessen the custom development pains and performs operations without taking more time.
For the best optimization of API calls and results in the “Where is this Used" button, the developers will need to write some code and functionalities.