You can Read more about Āvaṇi Aviṭṭam Here . Is the listed differences in the link exhaustive? And to the question, why so?
The reason is because the respective manuals (grhya sutras) have recommended each shakha/veda to perform the upAkarma on specific day which is followed by the respective veda and shakha people.
As per one of the Vaishnava legends, Lord HayAgreeva initiated Lord BrahmA in vedas during these respective days/stars hence we celebrate on specific days. (I do not have reference)
Rigveda Upakarma: Should be done on the day in shraavana where shravana is the star and spans at least from sunrise to mid day.But not in Uttara Ashadha if present during sunrise.
श्रवणे श्रवणायाम् उपाकर्म कुर्वीत आश्वलायन गृह्य सूत्र
Samaveda Upakarma: Should be done on hasta nakshatra on bhadrapada shuklapaksha
प्रौष्ठपदी हस्तायाम् वा श्रवणे श्रवणायां उपक्रमण= गोभिल गृह्य सूत्र
Krishna Yajurveda: i.e. Taittiriyas & Maitrayanis should do on shravistha, dhanistha,(avittam in Tamil),on shraavana month,whether it falls on purnima yukta Pratipada (Pratipat)during sunrise (Telugu- paadyami) or prathama.
Shukla Yajurveda: i.e. Vajasaneyi Kanvas and Madhyandinas do in purnima day if purnima is present up to evening.But if punima and pratipada both are present on next day(para viddha) they should do on previous day when chaturdashi stays in day and then purnima comes after mid day(purva viddha).Under no condition they should do/avoid doing in krishna paksha pratipat or broadly speaking they should finish upakarma before approach of krishna paksha.but they postpone upakarma to the next day if purnima is having Uttara Ashadha nakshatra.
श्रवणे पौर्णमास्यां उपाकर्म =पारस्कर गृह्य सूत्र
Atharva Veda: They do on the day when purnima lasts during sunrise.(udaya vyapini tithi)