If you follow a regular URL link from within Chrome (e.g. while browsing) while having the equivalent app installed, Chrome will Intent out into the installed app automatically.  You can try this with e.g. YouTube.

Physical Web, on the other hand, will always open the URL in the browser, which will then pop-out into the app after first navigation.

I think it is desireable to just deep link into app if it is installed, especially because of the "chrome-will-just-pop-out-anyway" issue.

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Some investigation which hopefully may help:

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The code to open URLs for PW currently looks like this: https://code.google.com/p/chromium/codesearch#chromium/src/chrome/android/java/src/org/chromium/chrome/browser/physicalweb/ListUrlsActivity.java&sq=package:chromium&type=cs&l=378


The code to open URLs for Chrome looks like this:
https://code.google.com/p/chromium/codesearch#chromium/src/chrome/android/java/src/org/chromium/chrome/browser/externalnav/ExternalNavigationHandler.java&sq=package:chromium&type=cs&q=ExternalNavigationHan&l=92

The Chrome code is convoluted because it includes handling a bunch of intent URLs.  We only need to handle https.  There are a few differences with Chrome's approach, not sure how many are necessary for us to adapt.

I think (to be confirmed) ultimately the code path ends here when doing an external deep link:
https://code.google.com/p/chromium/codesearch#chromium/src/chrome/android/java/src/org/chromium/chrome/browser/externalnav/ExternalNavigationHandler.java&sq=package:chromium&type=cs&q=ExternalNavigationHan&l=397


Some notes:

Chrome uses the "Intent.parseUri()" helper, which we do not, though its unclear if that is setting any extra parameters on the Intent.  It looks like it may automatically set a "package" on the Intent, based on this helper:
https://code.google.com/p/chromium/codesearch#chromium/src/chrome/android/java/src/org/chromium/chrome/browser/externalnav/ExternalNavigationHandler.java&sq=package:chromium&type=cs&q=ExternalNavigationHan&l=439

Maybe that is enough.  Or the real magic may actually happen in:
https://code.google.com/p/chromium/codesearch#chromium/src/chrome/android/java/src/org/chromium/chrome/browser/externalnav/ExternalNavigationHandler.java&sq=package:chromium&type=cs&q=ExternalNavigationHan&l=138

Chrome doesn't appear to set the CATEGORY_BROWSEABLE until later:
https://code.google.com/p/chromium/codesearch#chromium/src/chrome/android/java/src/org/chromium/chrome/browser/externalnav/ExternalNavigationHandler.java&sq=package:chromium&type=cs&q=ExternalNavigationHan&l=279

..and Chrome may be setting the Intent Selector, which we do not.

Chrome also appears to call startActivityIfNeeded() instead of just startActivity():
https://code.google.com/p/chromium/codesearch#chromium/src/chrome/android/java/src/org/chromium/chrome/browser/externalnav/ExternalNavigationDelegateImpl.java&sq=package:chromium&type=cs&l=292

Note about red herring: Chrome explicitly checks for available installed apps which can handle the Intent, and if none are available will link to the play store, but this only applies to non http intents:
https://code.google.com/p/chromium/codesearch#chromium/src/chrome/android/java/src/org/chromium/chrome/browser/externalnav/ExternalNavigationHandler.java&sq=package:chromium&type=cs&q=ExternalNavigationHan&l=287