I admittedly have not bought or used any of the bottled bacteria products. But I was curious to learn about them in how they worked and stayed alive in bottles, and did consider them as a safety back-up plan in case a tank crashed for one reason or another, so I have researched the bottled bacteria products and bacteria in general to get a better understanding though. I have always just used already established biomedia in established tanks to seed new filters/media, and if you have that option in sufficient amounts, I would personally recommend that approach (done this plenty of times, pretty much guaranteed to work if you know what you are doing).
Tetra SafeStart has Nitrosomonas, Nitrosospira and Nitrospira
Again I haven't had the product in hand, but according to the picture of the bottle it says an 8.45 oz bottle can treat 500 gallons, yet Drs. F&S said that size bottle treats 100 gallons. I haven't read the labels to know the specifics so I don't know which is the more realistic figure.
Aquarium StartUp: Ammonia Removal: Tetra SafeStart PLUS
Dr. Tim's One and Only has Nitrosomonas and Nitrospira
Dr. Tim is the one that first invented Bio Spira, which was later renamed Tetra Safe Start, and Dr. Tim created his own line of the product which is Dr. Tim's One and Only. And Dr. Tim is the one who did the scientific study to find out the what were actually the dominant nitrifying bacteria in aquaria (Nitrobacter was previously thought to be the main nitrite-oxidizers, but it was found out Nitrospira was). So I would automatically assume Dr. Tim's product would undoubtedly contain the correct species on bacteria and he only has the two predominant bacteria without the inclusion of Nitroso
spira so maybe his product contains more of the preferred bacteria than SafeStart. Dr. Tim also appears to be more upfront/honest about his product in explaining that the bacteria should be refrigerated to have a longer shelf life (slows them down to keep them alive longer). With that true comes more likeliness the stores properly store the bacteria, having a better chance the bacteria are actually still alive.
Setting up a new aquarium: Ammonia Removal: One And Only Nitrifying Bacteria by DrTim's Aquatics
This says a 4 oz bottle treats 60 gallons, so 8 oz would treat 120 gallon.
So for about 8oz of Dr. Tim's for $20 to treat 120 vs about 8oz of TSS for $10 to treat, let's say 100 gallons (if it truly treats 500 gallons with beneficial bacteria then it's a no brainer). The choice is up to you. I haven't used them so I can't comment further than the info. Whether you want to spend more and support the man (Dr. Tim) who found and created the correct bacteria formula or save an extra $10 is entirely your decision.
One thing to note is that the bottled bacteria, since they are stored in that solution and they are slowed down, they do function slowly, it is referred to saying the bacteria are "asleep" (essentially hibernating) and can take days to fully "wake up" and perform and reproduce at 100%. I asked Dr. Tim's team about this and they said it's true and the longer the bacteria are in the bottle, the longer it takes for them to wake up (among other factors, such as colder temps further slowing down the bacteria). However many people have reported using Tetra SafeStart and instantly stocking tanks with no issues (same should apply to Dr. Tim's), so this may be a moot point.
Using already established media from a trusted tank (disease-free water), you know for sure you are getting the right species of bacteria, and they don't require that "wake up" phase. You do need to use a reasonable amount of biomedia though to make sure you have enough beneficial bacteria. It is said that autotrophic bacteria (nitrifiying beneficial bacteria) multiply/double in 24 hours, so even using half the recommended bacteria amount ("awakened" bacteria), provide the necessary ammonia, the bacteria should grow to the size necessary within a day, same for your established tank you took the media from, it would recover even though you took half of the bacteria away (assuming you have enough surface area/biomedia). The 24 hour is the science to that anyway, which I haven't found that to be quite true in some scenarios I have seen, and yes temperature, pH, oxygen, etc do effect bacteria performance and reproduction (even on the bottled bacteria).
Haha, sorry if this went way more into depth than you were seeking for :P
In short, go with whichever you feel like, all of them should work fine.