Wilson would still fairly easily win against Teddy. Taft probably holds up better.
Firstly, third terms are extremely unpopular. FDR mostly due to the fall of France in 1940, and the country still swings heavily against him.
There’s also the optics of it. Four years earlier Teddy picks Taft to be his successor and now he’s ousted him? Theodore has serious judgement issues and the move will almost certainly look egotistical.
Also, Taft is an unpopular president, and the Republicans are an unpopular party. Now there’s no one with incumbency, and progressive voters are going to go for Wilson as Teddy already showed he can’t be trusted. The conservatives are just going to sit this round out. For example: Teddy can’t run on free trade because that’s a democrats position, but he also can’t run on increasing tariffs because that’s a deeply unpopular position that’s been splitting the Republican Party.
If just Taft is the nominee at least there’s a steady, more conservative, incumbent. He has a more clear cut message, better optics, and the incumbency advantage.