Hodu and Other Verses

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Overview

The minhag of saying Hodu as part of Pesukei DeZimra seems to have started in Eretz Yisrael as found in מסכת סופרים. The מקור for saying Hodu is already Seder Olam Rabbah which talks about David saying Hodu in the morning.

Hodu was not said in Bavel in the time of the Geonim and was adopted only later in Ashkenaz and France and then in Provence during the beginning of the Rishonim time. In Spain Hodu was added only later to Pesukei DeZimra. But, in Provence and Spain as opposed to Ashkenaz and France they said Hodu before Barukh Sheamar showing that it is not part of the main Pesukei DeZimra.

Introduction

After Barukh Sheamar we say "Hodu" which is the tefillah David said when he brought the Aron in Divrei HaYamim I 16. The same tefillah is found in Tehillim (with small differences). Why do we say the Mizmor from Divrei HaYamim and not from Tehillim, especially since most of Pesukei DeZimra is found in Tehillim?