It's impossible to tell you what is best without more specifics.

Typically, with a fixed lump sum fee, you and your architect need to be very clear on what it is that the architect is going to provide, and it needs to be spelled out clearly in your contract. Anything not spelled out in the contract will be an additional service (& fee).

Fixed lump sum fees are pretty standard for commercial projects or for small projects that are easily defined.

When we do a custom home design (yes, I'm an architect) we typically like to do it on an hourly basis and we give the client an expected range in total fee, which varies according to the complexity of the project. The expected total fee is expressed in terms of a % of total construction cost. We also give the client a breakdown of the expected total fee into the various phases of design so that we can show them throughout the project where we stand fee-wise.

Sometimes a client isn't comfortable with working on an hourly basis, afraid that we may run up a fee. If so, we usually will stay with the hourly rate, but offer a max fee we're not to exceed.