Congratulations, you understand the important distinction between activity and dose. This is something that many people (and news people) don't understand.
Activity (measured in Bq) is a measure of how fast something is decaying, but it doesn't say anything about the type of radiation emitted. Tritium and strontium may have the same activity, but they emit different types of radiation, and therefore have different levels of "harm".
Equivalent Dose is a measure of how "harmful" a type of radiation is. Equivalent Dose is going to depend on the:
- activity of the radiation (Bq)
- time spent with the radiation (exposure)
- type of radiation emitted (e.g. alpha, beta, gamma, neutron)
- energy of the radiation emitted (for example 1 keV vs. 10 MeV)
The units of dose are usually given in Sievert (modern SI unit) or the rem (older but commonly used unit).
Unfortunately, it isn't straightforward to convert activity to dose. Radioactive almost always emit more than one type of radiation, so you usually use a computer program to do this.
Another thing to consider is the biological hazard of the radiation. Some radiation passes through the body fairly quickly, and some radiation stays in the body for a long time. Strontium as absorbed by your bones and stays in the body a long time. Tritium is bound to water and passes through the body fairly quickly.
If you read about the effects of tritium, you will find out that the radioactivity effects of tritium are very low to humans. The radiation it emits is fairly low and it doesn't accumulate in the body. Most countries can't agree on what a "dangerous level" of tritium is because there are no cases of people being harmed by tritium. Strontium is a different story.