After the earliest years of pretty terrible quality of life, both the MA Bay Colony and Plymouth Colony stabilized relatively quickly. Without any feudal structures, individual families were able to own and cultivate their own land, and a quasi-market economy sprang up, bolstered by trade with Native nations and other young colonies in the Atlantic.

There were several big differences in class structure, as well as religion. In terms of a hierarchy, the quasi-feudal setup of England wasn't present in the 'New World', and, in part because of their religious ideas, the settlers actively resisted the construction of one. I'd argue-- and perhaps this is reductive-- there were two main classes, with variations within them. The bottom class would be unfree laborers: white indentured servants, enslaved Native people, enslaved Black people, and white/Native/Black people who were nominally free but formed a small captive labor underclass through forced apprenticeships, vagrancy laws, etc. Within this group, racial difference increasingly created a gulf between treatment of whites and treatment of nonwhites.* Above them was, well, the free laborers-- everyone else. Mostly white, this group contained initially family farmers, fishermen, and government and religious leaders. As New England developed, merchants, shipbuilders, and other specialized trades joined this group. In the 17th century, religious and civic leaders were the clear top of this free hierarchy, but, compared to most other European setups, it was relatively egalitarian. It is important to note, however, that their success was partially predicated upon the use of unfree labor.

New England colonists were Puritans, a relatively radical sect of Protestantism. Plymouth Colony (the 'Pilgrims') were Separatist Puritans, seeking a break from the state-imposed, Catholicism-adjacent official religion of England, Anglicanism. The MA Bay Colony did not consider itself separatist, but still sought to create a religious utopia (the oft-quoted 'city on a hill' refers to Puritan John Winthrop's vision for Boston). To that end, both colonies were, early on, incredibly conservative and tight-knit. Though the MA Bay Colony arguably pioneered a separation of church and state, social control was the name of the game, and the colony was oriented almost entirely around building a Puritan community. If it gives you any sense of how large religion loomed, Rhode Island was founded over a theological dispute. In other words, there were strong utopian visions prevailing throughout the first half-century or so of New England settlement. Sarah Vowell has a really delightful pop-history book on religion/society in early MA Bay, The Wordy Shipmates.

Other folks feel free to chime in. I'm rusty on my religious stuff at the moment.

Quick edit w/ another thought: I've noticed a feeling, among some people, that the early colonies were pretty damn alone. As a kid, I used to imagine them setting out a new settlement on the edge of the continent. But they weren't, really, ever alone. Like, right away the Pilgrims were engaged in diplomacy with Wompanoag leaders, and MA Bay Colony was sustained by its diplomatic engagements with Narragansett, Nipmuc, Wompanoag, and other nations. On top of this, the English Atlantic was, by the late 1630s, pretty connected. Trade between New England, Virginia, and the West Indies was common (if slow), and ties between these colonies were pretty deep. This is important because it speaks to the conditions at the time: these colonists had set up to create their Puritan utopia but were undoubtedly shaped in numerous ways by their connections to other societies and ideas. Also always good to knock down the old frontier myth.

*I've researched unfree labor in this time pretty thoroughly, happy to expand on that.