Very different careers. I'd be curious as to where you're seeing "museum science" offered.

Hofstra! Archive science, organization, etc.

Forensic science will lead to better paying jobs. Museum science is really interesting but there is so much competition for those jobs.

I personally would like doing museum science better, but practically I would go for forensic.

If $ isn't a concern, do whichever one you would be most excited to talk about every day!

I can talk to you a lot more about this topic if you're interested. Especially if you have a link to the Hofstra program (I Googled "Hofstra "museum science" and also searched the Hofstra site and couldn't find it - it's a very unusual term for US museum studies programs to use, which is why I asked. It's curious and an uncommon way of framing the different skill sets. Archives, collections management and conservation, for instance, use generally very different kinds of training). My career is closely related to this and I would be happy to give you a more detailed view of what the tasks and working life are actually like. Just email or Memail.

I'd be a park ranger except for what I saw Reagan do to that career field.
Likewise; arts are continually a treading of water except for the very best ( mix in a lot of history studies excellence, and a big -and- finding a museum that needed a person with such a specialty and it would work ), whereas all things police and criminal justice just continue to grow and receive more funds each year.
They both are kinda related; studies of past events; otoh I haven't read much about museum guys being killed a decade later by an angry customer that got convicted.
I'd say forensics for pay; the history/museum part as a hobby related to the actual career.