Should I use an app or edit my theme code for breadcrumbs?
If you want breadcrumbs that follow real parent categories, an app is the simpler route. Shopify doesn't record which collection sits inside which, so theme code has no hierarchy to show unless you build and maintain one yourself. Breadcrumbs adds that hierarchy without any Liquid.
What theme code can do
A breadcrumb snippet in your theme's Liquid can only use what Shopify gives a page: the product, the collection in the URL if the shopper came through one, and the page title. That is enough for Home › Shirts › Linen shirt.
It isn't enough for Home › Men › Shirts › Linen shirt, because the parent categories don't exist anywhere in Shopify's data. To show them, you would have to model the hierarchy yourself, for example in metafields, and keep it in step every time a collection is added, renamed or removed.
What the app adds
A category tree you arrange in the Tree editor, up to 10 levels deep, with display names for any crumb.
One trail per product, taken from your tree, and a Products page that shows each product's breadcrumb and flags the ones to review.
Ten breadcrumb styles and four long-breadcrumb modes, set separately for desktop and mobile.
BreadcrumbList structured data on every plan, and eight schema types in all on the paid plan.
Optional visitor-path trails, built from the route each shopper actually took.
How they compare
Setup: theme code means editing Liquid files on every theme you use. The app is a theme app block you add in the theme editor and save.
Theme updates: a Shopify theme update installs a fresh copy of the theme, so code edits have to be carried over by hand. The app block isn't part of your theme's code, so it isn't lost.
Removal: hand-written code stays in the theme until someone takes it out. Uninstalling the app removes its block, and your theme keeps working as before.
Speed: both are drawn in Liquid when the page is built. The app's trail comes from a metafield already on the page, with no extra request and no script (Visitor path, if you turn it on, adds a small one).
When theme code is enough
If your catalogue has only one level of collections and you are comfortable maintaining Liquid, a simple snippet can do the job. Once you want parent categories, a consistent trail for products in several collections, or structured data you don't have to hand-write, the app saves that work. It has a free plan, so you can compare the two on your own store.