In my experience, push and pull factors are strongly linked to one another. For example, a push factor is considered to be conditions that force an individual or a group to seek emigration to another country. A pull factor operates in the opposite manner, as something that "pulls" an individual or a group to another nation. For example, if religious freedom of expression can be seen as a pull factor, the push factor might very well be the inability to practice religion in a free setting. In this instance, push and pull factors operate in tandem with one another. In this light, immigration is seen as a convergence of both push and pull factors.
I think that the same premise applies today as it did back then - people come to "the New world" (although it is no longer new) because they are seeking an escape from something that they are leaving behind in their country of origin.Therefore, the push is to leave a bad situation. The Puritans were separatists (meaning that they had ideas that were not in line with the majority - in this case religious ideas - so they separated). They were being persecuted for their beliefs, so the push, for them, was to escape. Settlers in the Virginia colonies, on the other hand, had a different push - economics. They were n ot making as much in Europe and the new world was a land of economic opportunity. The pull factors, then, were freedom and opportunity. These are the same factors that drive immigration today. Many immigrants feel that the societies they live in are oppressive, the rules are unfair, the government is not doing its job. Others feel that America is a land of economic opportunity. In either case, the push is to get away from a negative situation, and the pull is a possibility of a more positive life.
I'm not sure why you have tagged this with "Mayflower Compact." Are you talking about back then?
If you are, the major push factor for the Pilgrims was the religious persecution (as they saw it) of Puritans in England. They felt that they could not run a godly community in England or the Netherlands.
The major pull factor was that there was the opportunity to run things their own way here in North America. They could have more of a chance to rule their own communities.
If you're talking about modern times. Both the push and the pull factors are much more economic. People tend to move from countries whose economies are weak. They try to move to countries with strong economies and lots of jobs.