As a general rule, files that are on the Internal storage and stored by your app (by default not WORLD_READABLE) will only be available for your application to read. When you try to pull these files using adb pull you will get permission denied on a NOT rooted device. There is a way to go around this, I will explain later. Files in External storage on the other hand, are available to the User and to all other apps to read. so it depends on what you are after.
Now in order to read files in your internal storage (/data/data/com.app.name) you cannot read these files directly, but what you can do is move them to the external storage and then read them from there like this.
adb shell "run-as com.yourappName cat /data/data/com.yourappName/files/myfile.txt > /sdcard/Downloads/myfile.txt"
Then you can pull the file from the external storage with no permission issues.
adb pull /sdcard/Downloads/myfile.txt
If you are unsure about which file or you want to browse all the files, then user the shell to browse all your app files.
adb shell
run-as yourappPackageName
cd /data/data/youappPackageName
ls -all