Sanchi stupa was well preserved and maintained by rules around that region. Europeans showed interest in Sanchi more than in Amaravati (Andhra Pradesh).
Amaravati stupa and Sanchi stupa were constructed by emperor Ashoka. Both were glorious and great cultures existed around the stupa. They were famous Buddhist centers.
When Buddhism declined in India and other religions got more publicity and practice, the Stupa at Amaravati had been neglected. It was buried under rubles. Dueing 19th centry a famous archaeologist Cole requested British authorities to preserve on site Amaravati, he was not heeded to. But for on-site preservation of stupa of Sanchi the British agreed.
A lot of plates and other items were taken away from Amaravati stupa to other parts of India and also to foreign countries including England.
Principles of preservation and importance of preservation of stupas was not well understood when Amaravati stupa was discovered. Sanchi stupa was discovered later and the importance of preserving was known and put in practice. Amaravati stupa now is just a mound, and does not have its past glory at all. Sanchi stupa retains most of the structure and inscriptions and sculpture.