As the backbone of modern economies, both local and international banking institutions have a crucial role in shaping and directing the financial landscapes. However, their respective mandates, regulations and impacts, often contrast. That's not to mention the influence they wield on the global economic environment.

In the first instance, local banking institutions primarily cater for the needs within their specific regions or countries. Despite their limited geographic scope, they hugely contribute towards sustaining the economic ecosystem through facilitating loans, managing deposits, and other monetary services within their jurisdictions. These institutions are indispensable to the growth of small to medium-size enterprises, as they provide them with critical capital and many other financial services.

On the flip side, international banking institutions operate beyond geographical boundaries, focusing on providing unparalleled financial services to a global clientele. They facilitate international trade by offering cost-effective and seamless cross-border financial transactions. Moreover, these institutions carry out foreign exchange operations, managing risks and creating a financial balance between the countries involved.

Amid the benefits, it's important to note the unique challenges and risks associated with both local and international banking institutions. From compliance with different regulatory bodies, managing foreign exchange risks, dealing with cyber threats, to coping with fluctuating economies- the complexities are indeed numerous. Regardless, these institutions continue to evolve and innovate, striving to provide their customers with vital financial resources while maintaining the stability of global economies.

In conclusion, the local and international banking institutions are not just financial entities but fundamental pillars upon which our modern economies hinge. Their collective function sees the global financial landscape regularly evolving and reacting to their decisions. These institutions, despite their unique challenges, are undeniably critical to the soundness and progress of our global economy.