Heat pumps are key in decarbonising the heating and cooling sector, while also supporting further integration of renewable energy resources when flexible heat pump operation is allowed. Within this context, smartly combining a heat pump, thermal energy storage and control system into a single product was introduced by the International Energy Agency and was named as a Comfort and Climate Box. Regarding heat pumps, manufacturers mainly include internal control constraints on the compressor ramping rate, cycling times, pump control etc. to ensure a safe and reliable operation. While these rules can generally not be bypassed, current literature mainly neglects or simplifies these control constraints, while the potential effects on the energy flexibility provision remains unknown. This leads to two main uncertainties. One the one hand on how flexible heat pumps really are when having to communicate from an overarching control system to the actual heat pump system, taking into account all the different internal heat pump control strategies. On the other hand, uncertainties also arise on which control aspects are of crucial importance to incorporate, even within a simplified heat pump model. Hence, this paper aims to experimentally investigate the effects of the on-board heat pump control in a Comfort and Climate Box system, while providing energy flexibility services, both for space heating and domestic hot water services. Comparison of experimental results retrieved from a hardware-in-the-loop set-up to results obtained from a simplified heat pump simulation tool for design energy flexibility evaluation showed deviations up to 17.73 % on the flexibility efficiency, 125.95 % on the charging time and 32.90 % on the discharging time. These results prove the requirement of incorporating the internal heat pump control for energy flexibility analysis, even within the design stage. Investigated aspects included the compressor ramping rate, back-up heater control, pump control, temperature measurement location in a thermal energy storage and the hydraulic integration of a thermal energy storage. Results show that especially the compressor ramping rate and mutual influence between the compressor speed, pump speed and back-up heater power cannot be neglected and should be incorporated in any heat pump model for energy flexibility analysis.