I am in sort of the "reverse" situation, at least from a BA perspective. I got my SK/*G Lifetime Gold in spring of this year which was a bit of a relief. I prioritise my BA Gold, and with the other one guaranteed I can now focus on BA easier. That said, even after hitting the 1,500 TPs, I fly oneworld wherever possible, as I appreciate the quality and service as top tier more than that of the Star Alliance equivalents, but it is nice to be covered on Star when oneworld is not a convenient option.
So guess my advise to the OP would be to go with what you prefer in terms of price versus quality. Star Alliance is huge these days, so should be fairly easy building up status there too if that is the desire (SK is pretty easy to reach Gold too).