1. Healthcare is heavily regulated. HIPAA is the most well-known law, but there are also countless local and state laws hospital systems must comply with.
2. Any new software needs to be sufficiently integrated with several existing systems and databases. What this means is that you can't just develop a stand-alone solution that deals with just one part of the process.
3. Many hospital staff are technophobic. Doctors especially.
I'm oversimplifying of course, but this is basically why incumbents (big co) are preferred. They have tons of domain expertise in healthcare, are deeply familiar with processes and requirements AND know plenty of people in the right places to grease the wheels when necessary. This makes it very difficult for startups to break into the industry.
I have no solid idea, but my impression from glancing at solutions for healthcare years ago wasn't that Hospitals are choosing Big Co so much as they have little choice.
As I understand it, smaller companies don't try / give up on keeping up wit the costs of required certifications (possibly the wrong term) and the like.
This also seemed to help explain the slow pace of advances and updates to such systems as patches and changes have their own onerous process.