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Let's not give the architects and those with the drawing and drafting skills the full credit for being urban designers. Yes, they have remarkable rendering, visualization, and presentation skills, however, some one has to write the urban design codes, regulations, and guidelines. And it's on this latter point where professionally trained urban planners can in fact impact urban design. But those trained in LA/UD/Arch have an inate knack for creating, drawing, generating computer visualizations, etc and probably end up doing the actual design. But depending on which sector these folks are from, the resulting final plan may or may not be what the designer intended. For instance, if you are an urban designer in the private sector, working for an architectural and planning consulting firm, you would do loads of drawing, interacting with municipal officials & and the developers, and more loads of drawing. But if you work for a municipality, I would imagine your work would be policy driven, writing about design objectives the local community wants, that is, writing the handbook for FAR, height restrictions, facde and signage requirements, etc, etc. You wouldn't actually do the designing, but your work would impact the overal design of the town/city over time. Further, in this role, your consultations to the planning board of commissioners could also affect how designs are modified as they are presented by developers to the commission.
But I don't know if I answered the original question posed. My sense, and this is the pessimistic side of myself, is that "urban design" is a new, fancy way of rethinking "urban planning," you know, to make it sound more glamorous and arty. It seems as if the new urbanists, and I'm talking about Duanyism here, the foaming at the mouth hardcore adherents of NU, believe that by revamping zoning codes with a visual guide and design standards that they are not merely "planners" but more than that, to be "designers." Since these new design guides have renderings instead of paragraphs and paragraphs about non-excluded uses, procedures for seeking zoning variances, etc, etc, ad infinitim, that somehow, the inclusion of pictures makes a planner a designer. ...hmmm... I'm not so sure about that. What do others think?
EDIT: Check out this thread, it is small, and I gave a long reply (and I do hope others respond! I want to know what other Cyburbanites think of urban design), but it does address the nature of urban deisgn, albeit from a British revitalization program POV: http://www.cyburbia.org/forums/showthread.php?s=&threadid=1197
If that's what it boils down to you for you, who makes more a planner or an urban designer, I'd say head back to school for urban design.
Urban design jobs in the public sector are really urban planning jobs. Most urban design jobs will be found in the private sector, and once you've gotten enough experience in design, you'll have the capability of making more money than an urban planner in the public sector, that is, if you're any good.
But remember, many young planners are infiltrating the local governments and are bringing elements of urban design they picked up in school, with them. For example, CPTED. It's difficult at times to get those who have been working in the public sector to appreciate these ideas, but slowly they will have to warm up to them, if they want to stay with the times and compete with nearby communities.
Urban design is more than "big architecture" or "small planning" - it is a unique discipline. Unfortunately, the ambiguity often associated with the profession leads many people calling themselves 'urban designers' after having taken an extra studio in architecture or planning school.
Urban designers must understand how buildings work, how units of a building are arranged, how parking access is accommodated, how construction techniques affect the building type. Yet they also need to know how the development process works, they must understand relationships between elements of the public realm and how to successfully shape them, understand the structure and order of cities, and bring together the community interests with the interests of the development industry. They also need to be able to draw, sketch, and imagine.
I work for an architecture firm as an urban designer and I use all these skills mentioned above daily. That's what makes it an exciting and rewarding profession. I have a graduate degree in environmental design (within a planning program) in which my area of concentration was urban design. This allowed me to take a combination of architecture and planning and yet still gave me the skills and knowledge required specifically for urban designers.
Good luck, hope this helps, but make sure if you do want to pursue urban design that you find a school that recognises it as a unique discipline, and not merely as an extra course under architecture or planning...