Early quantum computers are being offered by Cloud providers, with the ability to run Hybrid Quantum-Classical (HQC) applications that span Quantum and Classical (binary) computing resources. These HQC algorithms help benchmark and validate the performance of such near-term quantum hardware. Equally important is the software platform that allows a remote user to program the quantum computer on the cloud. The recent Qiskit Runtime platform from IBM allows a seamless and prioritized access to quantum backends and co-located classical hardware within their hybrid cloud for optimized execution of HQC workloads. In contrast, IBM's Circuit API offers finer application definition but the classical resources are not co-located but placed farther away. Here, we study and contrast the execution flows of a Variational Quantum Eigensolver (VQE) application defined using Qiskit Runtime, and an equivalent implementation using the Circuit API. We quantify the latencies of the various components in these execution. This offers insights on how to better orchestrate the execution of quantum applications across such hybrid resources.