You say developer, I say designer
The titles are some what interchangable in general language, but there is a really big difference. Depending on what you require choosing one of the other could leave you seriously out of pocket.
What does a website designer do?
Strictly speaking a Website designer will create a graphic representation of your website in Adobe Photoshop or Adobe Illustrator. He also may create what are called wireframes for layout and functional purposes. His next step is to build the UI or front end of the website in html or php depending on his still set.
For your basic sites this is fine as far as creating the look only of the site. The focus on the build is the look and not the behind the scences action. Often the do not understand the mechanics behind the scences and operate using a CMS Frame work like Wordpress to build most of there sites. (Note: There is cross over some designers are more qualified than others)
What does a Website developer do?
Developers do come in two flavours; frontend, which tend to be more junior roles in smaller companies, Backend, which tend to be more senior and they create all the database, fetching, performance tuning, calculations, Follow good SEO coding and all the stuff connecting the front end to the mysteries of the backend code in the server/s. Again there is crossover, however developers tend to find a preference either frontend or backend.
Normally the backend developers can build frontend without any issues from a mockup, but will often be dead in the water with out a design to follow.
Does it maker if I choose a designer
If your project is a simple flat html website, it is likely it won't matter. However, If you require a site that will organically be superior in Search Engines, load faster and be flexible long term you might want to look for a developer. The cost is often the same. However the developer can often offer more experience and expertise in the mechanics of what you are doing.
If you are wanting something like a store, database intensive website or custom build stick with the developer. If you need to hire an external designer then do that and keep it separate. Even if your website is a little ugly when it is finished at least the core of it will be sound and functional and the skin can always be modified. If you end up with a pretty site that doesn't function you are stuffed and the site will need to go in the garbage in most cases.
The attraction of hiring a designer
Designers and developers are often different people on the whole. Developers tend to be more introverted and quiet. They aren't outwardly excitable and they tend to qualify everything they say. Their promises tend to be measured and have clauses. Often something an excitable client with a hot new idea isn't attracted to. However often the developer is just as excited, but s/he is thinking about the mechanics of how s/he will do it rather than the excitement of the moment. The client experience of developers is often steril and flat. A client said I was like an old accountant once.
Designers are artist and on the whole they need to be more extroverted more passionate. They will be outwardly super excited about what your doing and get caught up in your emotions build it to a fever. They tend to be more agreeable and hopeful. All things that excited clients love and I don't blame them. Designers are like rockstars they make better sales people.
The common pit fall of hiring a designer
The pit fall of hiring the designer is sometimes they can get a little ahead of themselves and over promise leaving behind a mess or radio silence and an empty hosting account.
Every month we get calls from potential clients with stalled projects. The most common thing I here is...we started off so well, we really clicked s/he was really excited about the project the mockups were beautiful. Now its been 3-6 months and we have a couple nice looking pages, but nothing works! Now we are just going round it circles and nothing is happening...I think s/he is even avoiding my phone calls.
The situation is just classic amature developer stuff. Often inexperienced Web people and designers have this mentality: Well I learned html/css in just a few weekends and now its been years and I have made all these beautiful sites. Furthermore my clients say I am amazing. I use Photoshop, Wordpress/Joomola, Dreamweaver like a legend I can do this and if I can't I'll just watch some Youtube videos on php coding in the weekend and I'll be done in know time...and look at all the money, it's time I went to the next level.
The tech paradox
The tech professionals paradox is this:
It's so easy to learn, for a techie person, a good level of basic web design that is quite sellable. This small amount of knowledge is miles away from what the average laymen knows or can understand you might as well be a God at this point. However the problems start when you try to learn the other 99% of the online world.
I'll probably have my emailed trashed tomorrow, but web design is a lower level craft. Yes you can go to university to study it and there are the elite of web designer. Essentially though anyone can learn it online and if they have artistic talent they can do it. My arguement is your not going to pickup website hosting server design, by trial and error and feel. It's damn near impossible.
But all this stuff is online now days
Yes there is fantastic low level information available online. However some stuff just needs to be learned on the job as a junior or in a formal education environment or both. There is just no way around that. There is no youtube video for web hosting tricks, no youtube video for designing and developing huge databases for performance in enterprise environment and no youtube video for unique website backend design and there never will be. This area of the web is elite the information isn't freely available because often it is an unknown factor only solved through on the job trouble shooting in large environments, by highly educated or experience people.
As an example watch a video on basic website creation then watch a video on website and server security on the DEF-con channel. See how easy that was to pickup o.0 this is the same leap the designer needs to make to become a developer for just your project. You can make a wonderful looking website with basic skills. You can't even create a email form with low developer skills.
The Developer is often under valued
If you have a good developer everything will work 10x 100x better. Your SEO will work better, your user experience will be better and long term you will save money.
The Developer is the person who builds the foundation that will last a thousand years and the designer is the one who puts the plaster on, that keeps it fashionable.