EA is a navigator to guide the ship forward; and PMO is the steer to drive it through.
EA should have the highest level of vision over the enterprise. Therefore, EA can provide better judgment regarding portfolio initiatives as it has the more holistic view of the enterprise and the deeper knowledge sourced from the high and low level layers it covers. Nevertheless, it can always share its capabilities with the PMO in order to successfully and efficiently direct the enterprise portfolio.
It is more simply that EA is more as the planning phase and PMO is the execution phase. An EA life cycle is the starting point. The setup of a PMO might be one of the initiatives recommended as part of the EA roadmap. Once the PMO is established, EA would become the best tool for this PMO to steer enterprise portfolio for those initiatives that qualify as projects or programs. There are also those initiatives that do not qualify as projects. In such case, EA would, in addition to its role, play the role of the PMO and make sure such initiatives are implemented successfully
EA should play proactive role in project investment priority, business risk intelligence and change management, to ensure business effectiveness (doing right things), agility (capability to adapt to changes) and resilience (risk intelligence); PMO might ensure integrity of execution to original plan - alleviating the need for active involvement and engagement of EA. This would mean PMO is involved in QA and defect identification of implementation phase of enterprise design. PMO supports the execution of change initiatives which deliver the designs and initiative scopes EA produced, to ensure effectiveness of execution as opposed to quality of planning.
The other difference is that EA is usually focused on core business capabilities whereas PMO is focused on the change enabling and managing capabilities. So, they can both have this interest without being in competition with each other. Moreover, the subset of EA provides detailed technical insight that is necessary during the execution of the project and makes sure the architecture of the enterprise is preserved and adapted to the changes imposed by the newly implemented project.
Re-usability is of paramount importance in some organizations. Is it necessary this paradigm is driven by PMO or allowed to evolve from EA. Conventionally, these two groups are motivated differently to explore opportunities for reuse. The art of reusability is about architectural design thinking and strategic planning; the science of reusability is related to governance and in-depth analysis & calculation, to achieve business results such as cost effectiveness & productivity, and good for business' long term development.
Although there are functional differences between PMO and EA, look at it from a different perspective, both deal with the concept of portfolios, The PMO team and EA team should probably be joined at the hip and ideally report to the same C-level, with the common goal to achieve high performance business results.