I agree with you that the designs presented are much more appealing than your current design. While your current site is outdated and has a "responsive" (sort of...) design, there is a lot of room for improvement.
It looks like he is an experienced designer that has a working knowledge of SEO, which is really important when considering developing or designing a new site. URL structures, page layout, and usability all play into SEO.
As far as what design to go with, you'll probably want to sit down with your management team and first determine the following:
- Who is using your site?
- Why are they using it?
- What are potentials users looking for?
- What are we offering potential users?
After defining these answers (you probably already have done this), you'll have a better idea of what type of design you want, what type of call-to-action's you'll have, the layout and structure, etc., etc.