I could take a rough stab at what I imagine will be the left platforms position but to go into any detail would be needlessly taking the debate outside the party I'll leave it in outline.
The SWP's overall perspective is outlined regularly in our paper. That the economic crisis is not going away and many of the worst effects for ordinary people will either remain or get worse. That there is a pressure for the working class to pay (directly or via public service cuts) for the cost of the crisis. This creates a climate where class based resistance is more possible. Within the working class movement a section has been radicalised into taking radical action Lindsey (with all its contradictions), Vestas, Visteon, Leeds bins, Tower Hamlets College, pressure within CWU. This new spirit is in competing with the pressures of the TU's towards more beaurocratic methods of struggle, loyalty to labour and compromise. The role of the SWP is primarily to generalise these examples and bend all our energies into solidarity to help them win.
Following from this we are attempting to develop a generalised rank and file style network out of these disputes around the right to work conferences and demonstrations. One that can both link up and generalise struggles as well as providing a framework where people motivated around one dispute can get involved in future battles. We are also maintaining our work in around a number of political campaigns and united fronts (StWc, UAF and climate change primarily).
Part of adapting to the new situation has been to make the SWP's structures more ready for action. Both rebuilding branches as centres of activity locally and developing a younger cadre to take a more central role in directing the organisation at every level. Encouraging local areas to take their own initiatives and holding more regular educationals and day schools to give people the grounding in theory and confidence to fight their corner inside and outside the party. Basically rebuilding the Party, integrating newer members and asserting the SWP as a base for activity.
I would guess the comrades perspectives would differ over three things.
a) The relative centrality of the StWc. While obviously an important campaign I would be very surprised if the left platform didn't place the question of Imperialism on a near par with the economic crisis. I suspect they will also assume that if more emphasis was put into it local stop the war groups would be similar in size, diversity and appeal to the ones in 2001-2004.
b) A high stress on the need for a StWc style united front in response to the recession. The detail of this proposal I can't predict but a transferring of the model and alliances made I think is likely. I would suspect they will emphasis the political rather then class specific aspects of the crisis.
c) Model of leadership with big focus on initiatives from the leadership "driving things forwards." Strong emphasis on Party/united front's ability to transform the objective circumstance through bold imitative. This is the part I suspectwill be most clouded by the personal loyalty to various individuals.