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It's hard to be a splinter promotion. People watch a promotion because they like various things about it including the wrestlers, the booking and other things. You have to convince those people to like something else instead.
Historically, the splinter promotion does not do as well as the original promotion. See AJW and Original JWP, NJPW and Zero-1, AJW and NEO/Arison, Dragon Date vs El Dorado, NJPW vs UWF (multiple times), GCW and All-South amongst other examples. The promotion often has a good start but then slowly dies.
Sometimes, the splinter promotion can win out. See Nick Gulas vs CWA Memphis. NJPW/AJPW vs JPW
On rare occasions, the two promotions essentially tie - Noah vs AJPW and Michinoku Pro vs Osaka Pro.