I think this question is impossible to answer for several reasons...
1) The TM of today, and the CO of today, as well as all the rest of the molosser breeds, bare little resemblance to their ancestors. Perhaps they have the same coat color, or the same coat length, or some other general cosmetic trait like that, but for sure their personalities and looks have changed greatly over the past (1000s) of years of artificial selection.
2) Both breed's have bloated and hyped historical information attached to their "breed profile", with very little of it based on actual proven history and little facts to back up the claims.
3) The term "ancient molosser breeds" is a contradiction. There were no dog breeds in ancient times, there was no purity in their lines. The only thing that created a population that *may* have resembled a breed iwas geographic isolation - which was only an issue in the very early days of the dog-human cohabitation. Even in Tibet, arguably one of the most remote areas in the world, had travelers and traders moving through it with their own dogs (via the silk road) since 206 BC – 220 AD. Certainly these dogs have changed considerably since then, no?
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As for a temperament comparison, both breeds have a wide range. There are TMs and COs who are friendly to strangers and rarely guard. While there are also TMs and COs who are intolerant to strangers and very capable guardians.
In my personal experience, I've been less than impressed by the guarding of most of the TMs I have met in person (I've met around 20 TMs in person). However, I have met many COs who, while may be 100% bluffing, are rather impressive when guarding.
I think both the TM and CO has a high percentage of fear-biting and bluffing in the breeds. This is due to show people breeding dogs for the show ring, then placing them in homes as "guardians". There is a much larger show circuit here in the US for the TM than the CO, so one might assume that the CO would be less-refined in his/her guarding than the TM in the US... But, keep in mind, the CO is primarily a show dog in Russia, and is shown extensively throughout Russia and Europe - and all the dogs in the US come from these dogs that are being shown in the other countries.
I've owned COs for many years. I actually started my quest for an LGD-type guardian with true human aggression with the TM, but was unimpressed by the dogs I met in the US. I ended up going with the CO, and they served their purpose well for us - at one time we had 6 working CO on our ranch in Taos.
If one really wanted to own a dog more similar to the "ancient molosser breeds" of LGD, I'd probably look at getting one of the Central Asian Shepherd types - maybe a Tobet from kazakhstan where the dogs are not held to rigid breed standards and shown in dog shows and are still being mixed with sighthounds and other aboriginal dogs of the area to keep their workability and health.