As a matter of fact, to my humble understanding,
Adi Shankara only propounded Advaita as a matter of "Samatva" - one can reach God any way, because, Budhism was being misused and it turned out to be a religion contrary to the desire of Budha. The successors of Budha were only oriented in bringing down the existing beliefs, the rituals and they ridiculed them. Hence Adi Shankara only infused the necessary by introducing "Advaita - Samatva" He was never against Budha and his beliefs, he was only against the currupt practices of the followers of Budha.
We have heard in Nochurs pravachanams itself, about these, how Budha himself went into forest in his last years upset with the attitudes of his followers.
Infact, Adi Shankara's Paramaguru, Gaudapada, has freely quoted in his Karika references from Buddhist works of Nagarjuna and others.
Adi Shankara only infused advaita for a balance which was very much needed at that time of Chaos, Nobody were clear what to do, this or that, to leave rituals and leave family and kids to become a buddhist monk to attain Nirvana,

? What does one do?
It is in this time of crises that Shankara revived Sanathana Dharma, He did not go and convert people. He just said them the truth.
Where as in the times of Ramanuja, there was a BIG clash between Saivaites and Vaishanvaites. It was the need of the hour for Ramanuja to propound Vishshtadvaita because, people began to put Advaita into Action which is absurd.
Saivaites dominated over vaishnavites and reprimanded Vishnu. Hence the need of the hour was carried out by Ramanuja.
There is no difference between Buddha, Shankara and Ramanuja.
Salutations to Sri Ramana