Ben thinks that Presbys put more emphasis on the corporate aspect of church, while Baptists emphasise the individual and his faith. There is something in that, if we're just looking at what actually happens. But if we dig and try to do some actual theology from the Baptist side, I think we ought to find something like this: Baptists ought absolutely to emphasise the corporate nature of the church, but they ought to downplay the institutional structures of the church. For both Baptists and Presbyterians, the church exists because of calling. But this calling is understood very differently. The Presby, interpreting the NT in the light of the OT (a perverse procedure in my not-so-humble opinion), sees the calling of the church as being much like the calling of Israel. So, in history a group of people is called, and their calling endures through time and is passed on generationally. Baptism is rightly administered to children in recognition of this, and the church itself must have an enduring institutional structure to enable it to endure. It must exist above and beyond the individual congregation, and must have priority over the individual.
I submit the Baptist ought to argue that the calling of Israel is in fact a parable of the real calling of (Christ, and in him) the church. Therefore, the former is to be interpreted by the latter and not vice versa. The Baptist ought to maintain a much more dynamic understanding of calling. Church means gathering. It means the calling of people together, but in a very real sense this calling is never 'done'. Every Sunday is a fresh calling together of God's people. The calling of Christ - indeed, Christ's activity and rule in his church in general - is regarded as that much more immediate. So, yes, the calling of the individual has priority, but only because the calling of the individual is always into the body, and it is the calling of individuals that constitutes the church. This view of Christ's dynamic involvement with the church ought to lead to flexibility about institutions and even about individual congregations. It will also involve a recognition that church exists only as people are actually called by Christ into fellowship with him and one another in actual church life; therefore, to Independency. The Baptist understands Catholicity to mean that Christ is calling different people into different fellowships, and trusts that we are nonetheless called to and by the same Christ.
So Baptism/Independency is not more focussed on the individual than the community; it simply understand the community and its existence differently. This does have an impact on how we see children of believers - I think there is a category for those associated with the community but not yet called into it, a la 1 Cor 7, but this comes a long way short of the OT-ised view of the church held in confessional Presbyterianism. For which I am glad.