This has given me a lot more pause for thought than any 'Omnificence vs Absolute Destruction' poll. Thinking about it, beginnings and conclusions are just two sides of the same coin, and not just in that everything that begins also ends - for example, nonexistence concludes when existence begins, life concludes when death begins, etc.
Conclusion Dominance actually seems like a really interesting power. Think of everything you could do - sure, you can destroy things, but that's just so... bland. You can conclude your time in one universe by travelling to another, conclude death via resurrection, conclude something's nonexistence by bringing it into existence, conclude limitations by overcoming them, etc. You could conclude a lack of Nigh-Omnipotence to undergo Almighty Ascension.
Beginning Dominance can also do many similar things. You could begin your time in a new universe by travelling to it, thereby concluding your time in the previous universe, begin a life by bringing someone back from death, begin an existence (obviously), etc. You could begin your own godhood by undergoing Almighty Ascension.
Basically what I'm saying is that both powers can become Nigh-Omnipotent and really do anything, it's more preference as to how you want to do that. In my mind, Conclusion Dominance seems more innately versatile and interesting, though Beginning Dominance is easier to use and comprehend.