I don't think DS9 and Voyager split the fanbase in the sense that because there were two shows on the air at the time, each got lower ratings. I think it's just that neither one appealed to the broad base of fans that TNG did. If either had stood alone, I don't think it would have made a difference.
DS9 premiered to huge ratings on the heels of TNG. But very quickly, long before Voyager came on the scene, it's ratings trailed off. DS9 is a brilliant show, but it's quite different from TOS or TNG and it doesn't appeal to everyone. The people it didn't appeal to came, sampled and left and would have left regardless of Voyager.
Voyager tried to stick more to the TNG formula, often being referred to as "TNG Lite," but it always felt just like that... a lightweight version of the heavyweight that really worked. And it wasn't willing to take the risk of charting a different course for itself. So, again, it's numbers dwindled as the casual viewer's interest wasn't held like it was for TNG. And would have done so even if DS9 hadn't been on the air.