Most of the big sites of the world along with NewYork Times run on Wordpress. Please check this:

And it's world's most flexible, easy to manage, low maintenance and SEO friendly web platform as of now. So our vote is always for Wordpress. Solid code, robust updates, no headache, quick. Custom made sites are complex to manage and also depends on the local coder/programmer's efficiency and later years if you grow well, it's difficult to manage alone or by small team, whereas Wordpress is the DIY (Do it yourself) CMS (Content management system) with lots of great features.
So Wordpress in our opinion is always best for SMEs with low budget.  And there is a minor difference as Website and blog -Blog is frequently updated i.e more content i.e loved by search engines whereas Static HTML websites with 4-5 pages are now almost dead unless you have a strong offline business network & presence. With Wordpress, you can give your site look as a static website or as a blog ..that flexibility is solely on your choice and on choosing the theme. It's super easy to manage from backend.  The design completely depends on what theme you are choosing for Wordpress. There are various free themes as well as paid SEO themes framework available for use.