Just briefly looking into this, I would go with the identification in the article without marking uncertain. The key points being the Samuel Smith (s/o John Smith) bp. Burstall was married and had his children all born within 3 miles of his own birth place. While Ipswich is admittedly also close to Hadleigh, proximity absolutely favors Samuel son of John as the correct identification.
The second key is onomastics. John Smith of Burstall (in addition to son Samuel) had sons Philip and Nathaniel. Samuel Smith named a son Philip and had four grandchildren all named Nathaniel.
The article summarizes the evidence as: "The following evidence supports the identification of Samuel Smith, the 1634 immigrant, as the son of John and Mary (Gardiner) Smith:
• The 1634 passenger list shows Samuel as aged 32, which agrees with his baptismal date.
• He was baptized in Burstall, Suffolk, near Whatfield (where he married in 1624) and where his older children were baptized (Whatfield and Hadleigh).
• He was named in the wills of his grandmother Gardiner in 1615 and his father in 1618. Because he had immigrated to New England in 1634, he was not named with his brothers in the 1635 will of their aunt Elizabeth (Gardiner) Hayward.
• Samuel and Elizabeth named a son Philip, presumably either for his brother or her father (or both).
• Four of Samuel and Elizabeth’s six grown children named a child Nathaniel, perhaps for his brother Nathaniel.