If I may share my idea... derived from my modest experience... for easy management of the installed platform, I am of the opinion that you should use only one plugin with preference of the one distributed with the Moodle core. However, the H5P module (with blue icon) included in the Moodle core is still young and needs some improvement. The one managed by the Core Team H5P would seem to work better and in a more user-friendly way.
For example: I have two similar installations with both plugins installed, one installation with Moodle version 3.10+, the other with version 3.10.1+; well, on version 3.10+ of Moodle both components work without problems, on version 3.10.1+ the one distributed with Moodle freezes, without releasing apparent errors, asking to wait for the editing of the H5P component chosen in the library.
For example: I have two similar installations with both plugins installed, one installation with Moodle version 3.10+, the other with version 3.10.1+; well, on version 3.10+ of Moodle both components work without problems, on version 3.10.1+ the one distributed with Moodle freezes, without releasing apparent errors, asking to wait for the editing of the H5P component chosen in the library.