Is there any relation between each choosing those 2 dates.
Thanks. Any help is appreciated.
Although the Supreme Lord is beyond the nature of time and planetary influence, but still he acts in such a way that he is being influenced as a part of his leela.
For eg. See the verses of Valmiki Ramayan Bal kanda during birth of Lord Rama..
ततो यज्ञे समाप्ते तु ऋतूनाम् षट् समत्ययुः |
ततः च द्वादशे मासे चैत्रे नावमिके तिथौ || १८-८
नक्क्षत्रे अदिति दैवत्ये स्व उच्छ संस्थेषु पंचसु |
ग्रहेषु कर्कटे लग्ने वाक्पता इंदुना सह || १८-९
प्रोद्यमाने जगन्नाथम् सर्व लोक नमस्कृतम् |
कौसल्या अजनयत् रामम् सर्व लक्षण संयुतम् || १८-१०
विष्णोः अर्धम् महाभागम् पुत्रम् ऐक्ष्वाकु नंदनम् |
लोहिताक्षम् महाबाहुम् रक्त ओष्टम् दुंदुभि स्वनम् ||१८-११
Twice six months had rolled a way since the great sacrifice was over and, in the first month of the New Year, on the ninth day of the bright fortnight, the Lord of the worlds chose to take human form and sent down half of His essence as the son of Kausalya (thenceforth to be known as Rama), the world-honored One, the crowning glory ot the grand line of Ikshwku, and the sum of all perfections. The constellation Punarvasu, of which Aditi was the regent, was chosen to preside at his birth. The Sun, Mars, Jupiter, Venus, and Saturn were in ascension in their respective houses. Aries, Capricornus, Cancer, Pisces and the Libra, Jupiter and the Moon were in conjunction ; the rising sign was Cancer. And KausalyA, shone with unparalleled effulgence, even as Aditi when she gave birth to Indra, the lord of the Shining Ones, the Vajra-wielder.
See here the nature of planets. All planets are in exalted position. Lagna was karkata (cancer). The kundali of this time and latitude( Ayodhya) best fits in describing characters of Lord. This would only happen on particular tithi and particular time of a particular place in particular year. Hence lord Rama choose to born in that particular tithi of that year. Similar is the case of Lord Krishna.
In 10.3 of Bhagavatam..
>1-5. Thereafter, at the auspicious time for the appearance of the Lord, the entire universe was
surcharged with all the qualities of >goodness, beauty and peace. The constellation Rohini appeared, as
did stars like Asvini. The sun, the moon and the other stars and planets were very peaceful.
Hence that particular tithi ie. Krishna Ashtami (ie. Rohini nakshtra) of that year was the one which could best describe qualities of Lord in that particular place and particular time as described above in case of Lord Rama.
Hence Lord chooses to born in such time, place tithis and nakshratas. Destiny exactly prepares the condition of time and place for their parents and other by the virtue of their prarabdha karmas.
Hence although Lord is capable in stopping influence of planets but still to keep the words of Great Astrologer Sages true Lord comes in such time at which planetary positions best describes his virtues.