It really depends on your website however, if you are in an industry in which "speed" is important then, Live chat is a must. There are many studies showing that people expect an answer during the first 30 mins of submitting your inquiry or issue to resolve. If you don't resolve or answer within that time frame you start to loose customers, making speed very important. But, if your business is not really related to that kind of support then I'd advise a contact us page.
Now, I must say that the speed in which you respond is very important no matter the business. The ability to resolve issues and respond to questions define you as either a good company or a GREAT company. And great companies like Apple respond within 30 mins. Now there are cases in which takes a little bit longer but great companies usually resolve within 1 hour if the "issue" is not that important.
So, it really is up to you to determine which is best for your business. If you are in a business where you only provide information then I recommend a contact us page. However, if you are in a service environment then I highly recommend a live chat.
Hope this helps you choose which to go with.
