Is the success of the model a threat to Western powers. If so, how so?
Possibly, the extent of which is hard to quantify, but there are certainly relevant factors.
Africa may not seem that relevant to the West, but it is certainly important in a few ways. Firstly, it's near an important shipping route. When looking at ships going from China to Europe Africa is somewhat in the middle. Secondly, Africa may have rare materials (e.g. specific minerals) that are important for advanced technologies.
As such, China's involvement is not necessarily a threat, but it does give them more power geopolitically.
Is this success a good thing considering that its model of economic development was based on the Chinese model?
This touches on another issue. More closer to the West, in this case NATO. Shadow1024 correctly uses the term white elephant to refer to Chinese investment programs abroad. To following quote from The Diplomat explains how some see this as "debt-trap diplomacy":
“Some believe China engages in ‘debt-trap diplomacy’ through the BRI, ensnaring developing countries with debt dependence and then translating that dependence into geopolitical influence,” says Paul Haenle, former U.S. government adviser and director at the Carnegie-Tsinghua Center, summarizing much of the critique.
“Particular concerns around China’s actions in Sri Lanka, Pakistan, and Malaysia are central in the debt trap debates. China acquired 99 years of operating rights for the Hambantota Port in southern Sri Lanka after costs for the project spiraled out of control, forcing Colombo to give up control of the port in return for a Chinese bailout,” Haenle explains.
So, where does NATO come in? Montenegro, a non-EU NATO member actually has also made such an investment deal with China. From the Jason Institute:
Montenegro is among the most vulnerable nations to accept Chinese loans. The loan for the first part of the highway will likely result for Montenegro’s debt to rise to 80% of its GDP. This has caused EU officials to fear that the tiny Adriatic republic will become entangled with China’s ‘debt-trap diplomacy’. This is similar to a scenario that unfolded in Sri Lanka when Chinese investments reached $1 billion. The government was forced to hand over a port in the Pacific Ocean as part of compensation efforts. A similar situation also happened in Djibouti, where as a result China opened its first military naval base abroad in order to ‘protect Chinese investment’. A Munich Security Conference report stated that about 40% of Montenegro’s total external debt – the highest measured percentage – is destined for China. There seems to be evidence that China invests where it knows that the loans are highly wanted, but unlikely to be paid back.
As you can see, China's Belt and Road Initiative takes place in many countries and as such it has a lot of geopolitical impact. Combine that with the difference in form of government and ethics between the West and China and it's certainly something that has the potential to harm the West's interests globally.