I'll be honest - your vendor should be taking into account your current and projected platforms, as well as your branding requirements and Informing you what the best option is.
Your future hosted provider may or may not support Apps and/or sandbox solutions. These are configurable and can be turned off. If you are looking at O365 - then both are available and both are supported. I would ask your vendor how many of each solution they have developed and deployed. If they have not done app deployment than you may incur the "learning curve" along with them.
That being said Microsoft will recommend you utilize the app model. that doesn't mean it's the only or right choice for you however and depending on how it is developed this may require an additional web server/host for remote components.
I would site down and do a pro / cons list with your Vendor. Start with the outcome you desire. After that work in the assumptions on restraints, such as environment, maintainability, etc. Next the Vendor can help layer in the technical requirements for each solution and then make the best choice.
Consider these questions:
- Vendor maturity with the proposed solution.
- Current and Future state of your platform.
- Additional requirements and costs.
- How will it be maintained (applied to new sites, updating artifacts, enforcing It's use, etc).
- Consider what was requested to be branded vs. what Microsoft recommends, and why (did you ask for the suite bar to be branded? This has implications with O365).