Both are vast networks buzzing with customers and you should take advantage of their advertising potential. I have been using both as advertising platforms with very good results. Maybe you should consider setting up a Business Page on both LinkedIn and Facebook and see how they convert for your products and services.
If you already have a presence in Twitter, Google+, Facebook, LinkedIn, you need to put them to work for you. Social media marketing is here to stay, and there are some great tools out there that will bring you followers and more business in every single channel. You should tap into every social channel available, and there are tools to help you coordinate your social media marketing efforts using those channels. I can devise and executea social marketing plan and either maintain it for you or deliver it to your team to continue: deliver content, social media ads, social listening, engaging with prospects, there are all essential elements to reach success.