Depends on the church and the time.
The Particulars gained the upper hand in England by the 18th century; many of the Generals slid off into Unitarianism or other beliefs, and only the establishment of the New Connexion in 1770 was able to reunite the Particulars and Generals and, probably, save the Generals from extinction.
It is true that the New England Baptists were more General. I suspect that a good deal of the impetus toward the doctrines of grace came from the New Light movement, in which many Congregationalists moved toward the Baptist churches and took their traditional Puritan leanings with them.
Now, I'm not sure how you prove what "ordinary" Baptists held to throughout many of those years. The Separate Baptists, many of whom came through the New Light movement, were practically as Particular as the Regular Baptists, as is evidenced by the writings of the Regulars about the Separates. It was the preaching of Whitefield, a Calvinist, that appeared to fuel the growth of the New Lights and Separates, so it's only natural they would adopt that soteriology.
A brief examination of the creeds and confessions will testify that the vast majority of them were Particular. Even today, the SBC's confession is Particular, though in a waffling way (and totally in line with the New Hampshire confession.)
My own hypothesis is that Baptists were highly influenced by Methodism and Campbellism (with whom they were competing on the frontier) the rise of the revivalism movement, and (among Southern Baptists) a lessening emphasis on soteriology caused by the rise of conventionalism.