Flexibility

As a freelancer, there is much more opportunity for being flexible when it comes to working practices. This isn’t just in the arena of timekeeping, where obviously the freelance designer is more likely to be interested in working outside of regular office hours, but also in general working methods. A freelancer, for example, is more likely to be willing to experiment with new ideas – if you want them to – and will be much more open to making multiple changes until you’re happy, rather than necessarily charging a fee each time you want to see what the design looks like in a slightly different colour or with slightly larger text sizes.
WINNER: Freelancer

Affordability

Freelance web designers, essentially being self-employed, are much more likely to be able to provide a high level of service without having to charge the higher prices associated with agencies. Most freelancers won’t be having to pay for a large office, multiple members of staff, accountants, lawyers, administration staff, etc., plus the agency will almost certainly employ a sales team/salesperson that needs to be compensated for their time in generating your business – usually through some kind of commission arrangement. Whereas a freelancer will often generate their own new business, thus being able to dispense with the higher fees associated with commissions and sales bonuses. Overall, freelancers will be much cheaper and very common to go for, especially for small/ start-up businesses.
WINNER: Freelancer

Time Constraints

When you are working with only one person, it can be difficult for them to fit you in with their other clients – there are only so many working hours in a day after all with a freelancer only being one person. An agency would have multiple members able to work on many various tasks on your project simultaneously. Personally, I will counter this by making sure my time is appropriately managed down to every minute and, I will not take any project I am not 100% able to meet the requirements of.
WINNER: Agency

Scope

For the majority of web projects, a freelance web designer should be able to fit it into their schedule and deliver it on a golden plate. The quality of the website would be the same, just cheaper. Though in certain cases, where your website project involves many layers of functionality and involves a much larger scope than your typical website (let’s take Amazon for example). Your best bet is going to be an web design Agency that has a ton of resources and time at their disposal and can have people of many different talents to come together in order to create a functional website that meets goals in a reasonable time. You’re probably never going to see one person take on a project of that size. Probably.
WINNER: Agency

Communication

When using a freelancer, you are going to be dealing with the person who is actually creating your website, the person who actually makes the decisions – rather than having to go through multiple layers of administration before sorted like you would with a large agency. This is particularly useful for when you want to ensure you get things done the way you want them to be, rather than having to wade through an endless wave of minor alterations before you finally settle on something suitable. The ability to talk directly to the person that’s making the changes to your site is one that is very valuable and is the hallmark of the independent web designer, rather than the web design agency.
WINNER: Freelancer

Conclusion

Many businesses (especially small and start-up companies) are much more suited to go with freelance web designers for their flexibility and affordability, whereas some larger companies may have a much broader scope beyond that of which one person can handle and would look to an agency for. These are just a few areas covered, there are many more factors that might influence your choice. So really, it all comes down to you and what your requirements are.
WINNER: You