Earlier quoted context omitted.
It's an alpha emitter (and if being used in a university classroom, probably a sealed one). Unless you eat it, the danger is not comparable. Radium, in contrast, emits gamma radiation, which presents more of a threat to casual bystanders. All of which is to say: you can't just compare "radioactivity" levels and extrapolate to "danger".
I'm more scared of alpha than gamma. If the alpha source gets tampered with and becomes a dust somehow, it could stay in someone's lungs, and kill someone without being easily detectable. Cheap eBay Geiger counters will probably tell you if gamma rays are an immediate danger, and if you're close enough to have problems, your probably also close enough to detect it.
It's not an either/or sort of thing. Gamma decay occurs after alpha or beta decay, so a gamma source will also emit alpha or beta radiation. In the case of Cs-137, it emits a lot of beta radiation. Normally this is shielded, but normally it doesn't fall off a truck..