I see. Nice rankings for both.
In my personal opinion I would go for the inner page as a main landing page for that term. The reason why is you have liberty for this page to make it more friendly for google - it has a better call to action in my opinion so it can convert better.
If you are able to improve it as far as content it can rank even better - but that won't be enough.
What I would do additionally is to add a predominant link in the home page to this page like adding a box of content in the body of the home page and link crime sceme clean up to this landing page.
If you can go into more details on the landing page about the service it will help - but don't over crowd it.
Some social signals will help - I just plus one it but that is not enough Get some signals there .
Some new freash links - editorial if posibile will also help a lot.
The other option of course is to ad rel canonical on the inner page and keep the home page as primary - the easy path.