"Environmental health and safety" is a bit of a broad descriptor IMHO. I started my EHS career back in 1990 and most of our software, checklists, and training programs since then have been written in-house. Most of my work now is in audit & compliance and contractor safety, but those subjects are only two of the several EHS fields I'm aware of and most of the companies I work with have gone to web-based solutions to supplement their in-house solutions. Being in the US, I only deal with OSHA and Federal requirements.
My only two comments regarding Verse Solutions are that the company seems to not have a defect tracking solution (being in construction, both I and my clients require defect tracking - and not just in an Excel spreadsheet...) and, more importantly to me, they've been in business for less than 3 years - not a long history of success or failure, and that most of their clients seem to be services- or process-oriented and not manufacturing/construction or de-construction/labor oriented.
And, also importantly, I prefer Enablon's 15+ years in their chosen field and likely wouldn't hire an SAS company with less than 10 years in business in order to see their legal history and company stability. But that's just me. EHS solutions are too important to what I do now. A comparable explanation is hiring a civil/structural engineer now - there's no way I would hire a new PE with less than 5 years of field and office experience. Good luck.