I doubt the premise of your question.

Economically speaking, in terms of things like Human Development Index or GDP per capita (PPP), Gabon Botswana is (in 2017) roughly equal to other African former colonies like Algeria, Tunisia, Libya, Seychelles, Mauritius and Gabon.

Seychelles and Mauritius are both Indian Ocean island republics that are heavily reliant on tourism for their economies. And, in full fairness, Seychelles has a very small population of under 100,000 people. On the other hand, Mauritius' population of 1.2 million people is more comparable to Botswana's population of 2.2 million.

In some ways, Gabon's economy is similar to Botswana's, both being underpinned by resource extraction. While Botswana's primary resource is diamonds, Gabon is a significant exporter of petroleum. In terms of population, Gabon has about 1.9 million people, so slightly smaller than Botswana.

Turning to the other aspect you name: political stability. I'm going to be presumptuous and assume you are speaking of political stability with democratic norms. And to be sure that has been a difference that makes Botswana stand out in comparison to other countries I have named.

I think it is fair to argue that from 1960-1998, Tunisia saw an undemocratic yet stable political system under the long tenures of Bourgaba and then Ben Ali (with the exception of Ben Ali's overthrow of Bourgaba in 1987).

Similarly in Gabon, the country was first ruled by Leon M'ba from 1960-67. Following his death from cancer, his Vice President Omar Bongo would go on to rule as president for the next 42 years, passing through several non-competitive elections.

The Seychelles and Mauritius have histories in the 1970s and 80s that feature power struggles between political factions, and in the case of Seychelles an attempted mercenary coup.

So, yes, it is fair to say that Botswana has a longer tradition of credible democratic elections and presidents observing term limits, rather than dictators with extremely long tenures. That difference has perhaps made Botswana an attractive model for Western diplomats, political scientists and development experts to hold up as a "success story" of economic growth AND democratic norms.

On the other hand, I will also observe that every president of Botswana has come from one dominant political party [Edit- additionally, the Botswana Democratic Party has controlled a minimum of 2/3rds of National Assembly seats in every election since independence] . Also, by GINI coefficient (an estimate of wealth inequality), Botswana compares unfavorably to Gabon, Seychelles and Mauritius, meaning that there are greater differences in wealth between the poorest Batswana and the wealthiest.

TL;DR- Botswana has been successful, but perhaps not head-and-shoulders above the rest.