Thank you for the opportunity to help you with your question!
I would apply parallel method for implementation phase as it provides me the flexibility to carry out development and implementation of different modules which would be interlinked later on to form the complete system.
Phased method could be used for complex projects where we need to divide the implementation in parts and all these parts have to be implemented sequentially for complete implementation of the system.
Please let me know if you need any clarification. I'm always happy to answer your questions.