You only need one of them, they are essentially the same bacteria. Unless you wear a belt and suspenders
I prefer the Dr. Tim's and have never tried the SafeStart. But the company that owns Tetra also shares the patents on the product with Dr. Hovanec aka Dr. Tim. He developed it.
Also, they have different instructions for how to use their respective products. When using Dr. Tim's it can take a week to have a fully cycled tanks but is usually more like 10-12 days. What you will be doing is waking them up and then cranking them up. In the bottle they are dormant. Having oxygen and ammonia available cause them to go back to work.
There are three ways you can use either of these products. One is as directed, i.e. using the right amount for one's tank. However, the second way lets one buy less and save money and take a bit more time to get them to double. That is, if one has a 50 gal tank, they would use a bottle for 25-30 gallons and use ammonia to get them to double. the third way is to accellerate the process by getting more than the normal amount and buying more. For example you get enough for 60 gallons to put in your 30 or 40 gallon tanks.
However, if you buy the correct size the only reason to add ammonia is to wake them up. That should be enough to stock the tank pretty quickly. Not everybody has similar parameters and tanks. So what is in one's tap water will vary. A Enough oxygen and carbonates (what makes KH) matter as well. Finally, one's water temperature an pH can have an effect as well.
Pretty much any of the cycling products that contain live nitrifying bacteria tell users to maintain pH above 7 and up to about 8 I think. Most tell you to turn off tank lights and UV. All that do not contain Nitrospira (they use Nitrobacter) also want you to do multiple additions in the first few days of weeks. The ones with Nitrospira will tell you to shake the bottle well and then pour the entire thing into the tank. But they also want more of your money and will usually suggest yo can add it if wou add new fish or water a water change. You do not need to, save your money.