With my personal experience, I'm going to spill some dirty secrets of IT consulting firms in order to let you seek the right IT consulting firm rather than best consulting firm.  First recommendation is to ignore the superlative terms like "BEST" as mostly such terms are used by people vying for your business. High frequency of use of superlative terms represents that either they are falsely claiming or truly leading in business. Whatever the case is, trust me you wouldn't want to work with either of them after reading the following suggestions.

Let's suppose you chose the "Best" IT consulting firm for your business, following are the expected outcomes.

1. They are often over-committed and under delivered. Saying yes too often is their business which leaves them over-committed and ineffective. If they're already BEST, they don' feel the need of constant improvement which can directly affect the delivered end product. They tend to seek every project they get even though they don't enough workforce to handle such amount of project which will result in ineffective development and delivery of your website.
2. You're not THAT important. Let's suppose BEST IT consulting firm is working for your website and to manage to fulfil their minimum requirement criteria, they will still treat you as a small account. You will have to manage according to their flexible and may not give you the attention and recognition you deserve.
3. They're highly Expensive. It is obvious that with popularity comes the expense. You might have to overpay them as they will cost you minimum of $150 K, depending on the requirements of your website. Worst part is you will still not get the best of them as it is obvious they reserve their best talent for bigger projects. So, you're mostly getting services from junior talents or worse, interns only.
4. They're trying to get done with you ASAP. If you're unlucky enough, they might be working on a bigger project bagged from Fortune 500 account and you're just a hurdle in their bigger project. At this point they want all their focus and account on the bigger project and will try to get done with you quickly which will obviously result in unsatisfactory delivery of the project.
5. They will make you listen rather than listen to you. Obviously they seek expertise in what they do, which makes you unable to raise your voice regarding doing things differently or be creative. In fact, they know what they're doing and you should just sit back and watch. Maybe if you're lucky enough, you might get chance to "whisper" a few things.
6. Your testimonial is not always important for them. If you are small level business and doesn't make the list of their biggest client they might not even care to maintaining relationship with you. Currently, they see you as sales figures only and won't even engage with you any further. Harsh but truth, you are just a one night stand for them. Moreover, if big fortune 500 companies are offering them testimonials then your testimonial might won't even make to their website.

Now, let's suppose you chose the right one instead of best one, what will you experience now?

1. They will go extra mile to deliver the work they committed because you're an important client for them.
2. Best of their talent is working for you and the bill rates are relatively lower than the BEST IT-consulting firms.
3. As you're important for them, they will focus on every aspect of your business and will fulfil each requirements respectively.
4. You are in better negotiation state and they will focus on delivering the satisfactory end-product.
5. They will try their best to deliver their work with creativity and differently to impress you as you're important to them. They will be flexible and will acknowledge your demands/requirements.
6. You can expect more strategic partnership with them for a long-term relation stability as they want to work with you in future also. your testimonial holds importance as it might promote their business.