Adam,
I don't know what design field you are in, but in golf design, the short answer to your question is YES.
Right now, I am interviewing for a few renovation projects in the same area. One is the best club in town, seeking the very best playing surfaces for a limited number of rounds. The other is a muni looking to upgrade the look a bit, but also with maintenance in mind, high play, etc.
Naturally, my sales message will be tailored to their specific needs, which are vastly different, and if my message isn't right, I won't get the job! If and when I get one or the other, then its easy to see how my design proposals will be vastly different.
The one thing they both have in common is the need to know "how easy we will be to work with." That usually means, will we force our ideas on them, or will their input be accepted as part of the process. Any good architect, up to and including, say Tom Fazio at Shadow Creek, will usually take specific good input fromt the Owner, in addition to following their general goals, while naturally trying to keep them from doing something that won't work, and giving them the very best design possible.
The third way the Owner influences the project is, of course, by providing a budget equal to his goals, whatever they may be.....