What is more important to visit the place where Tsaddik buried or where he was born?

Shalom, Thank you for your question. Your question is an interesting one, but first let me address the question that you didn't ask – is there an importance in visiting sites where great and holy Jews were born or died? While there are certainly sources in Judaism that do encourage one to visit the graves of Tzadikim, it should be stressed that this is not a command (mitzvah) nor even a custom that is widespread amongst all religious Jews. That is to say, that while one may want to pray to G-d at such a site, one should not feel that there is any obligation to do so – nor is prayer in other places “worth less”. For example, praying with a minyan, praying in a synagogue, all the more so praying at the Kotel, all have great value. In fact there are sources that place praying in such places on a higher level than praying at a grave. None the less, as I wrote, there are indeed sources that stress the value of praying at the graves of Tzadikim. This can be found in the Midrash that tells of Kalev (the good spy together with Jeshua) who went to grave of the Patriarchs and Matriarchs in Hebron to pray at their graves. Throughout Jewish history there has been such a practice, and it is even mentioned in the Shulchan Aruch (for example before the High Holidays, and on Fast days). If a person feels a desire to pray at such a grave, they will be joining their prayers with countless other righteous Jews who have poured out their hearts to Hashem at such sites all over the world and throughout Jewish history. Now to your question – is it more important to visit the site of the birth or burial of a Tzadik? While there are several sources that mention the graves of the righteous, this is not so when talking about the place of their birth. I know of no widespread practice to visit the places where great Jews were born. In fact, the birth place of most the Tzadikim is not marked at all. Even those few that we know about are not considered as particularly special places to visit. For example, the Ari HaKadosh was born in what is today the Old Yeshuv Museum in Jerusalem, and even though there is a synagogue there today, it is not known as a special place to visit and pray at. So, the answer to your question is that it is more beneficial, and more widespread, to pray to G-d at the graveside of a Tzadik, rather than where they were born. Blessings.