To some extent it's not entirely clear - in fact, the Council of Europe addressed this in a recent report from the body's High-Level Reflection Group:
The group takes note of the ongoing discussions, among European Union member states, on a future “European Political Community” (EPC) which remains to be defined at the time of writing this report. It notes that such a pan-European political community already exists, in its areas of expertise (human rights, democracy and the rule of law), and it is embodied by the Council of Europe. We therefore recommend a proper articulation of the role of any future EPC and its relationship with the Council of Europe, taking into account their respective areas of intervention. To this end, a joint declaration at a fourth summit could clarify the respective roles of the Council of Europe and of a future EPC.
We can conclude from the first meeting of the European Political Community, however, that so far it seems to be a much more informal summit, structured around fostering conversation between leaders outside of the more formal institutions of the Council of Europe. There is no Parliamentary Assembly, for example, nor a Court of Human Rights. In addition, there was no joint memorandum published after the summit's conclusion - reinforcing the idea that the meeting was intended to foster frank discussions, rather than focussing solely on reaching agreements.
This seems to match up with the objectives for the body discussed at the European Council meeting in June: "to foster political dialogue and cooperation to address issues of common interest so as to strengthen the security, stability and prosperity of the European continent".
Another meeting between leaders has already been pencilled in for Spring 2023. In contrast, the Council of Europe's top-level body - the Committee of Ministers - meets just once a year, and consists of the foreign ministers of member states, rather than the premiers. There have only been three summits of heads of state and government of the Council of Europe - the last being way back in 2005.
In some respects, it remains to be seen whether the EPC will complement the Council of Europe or overlap with it, but so far it seems to be fulfilling a distinct role in the sense of getting top-level decision members around a negotiation table.