The Obama version is better than what Republicans would have ever come up with in various ways, but it is still true that the ACA is, basically, a conservative private-sector focused health care plan with some public sweeteners that were put in largely to make the bill have a better CBO score (lol).
They don't have a plan because you can't make it "more Republican" and "better/cheaper."
"My plan would reduce your insurance premiums by stopping government payoffs to big insurance companies and sending that money directly to the people," Trump said in a video announcing the plan."One-page fact sheet."
However, the video and one-page fact sheet posted on the White House website were light on specifics about how much would actually go to Americans or how much funding the plan would require or how the funds would be distributed.
To make real whatever is sloshing around Trump's pudding brain, you'd basically regulate all prices and dissolve the insurance companies. Essentially it'd be Medicare only you'd get the bill. Of course Republicans can't do that.