Conservative-I-can-reason-with Noah Millman observes that "Leaving the specific details aside, Ryan’s and Obama’s health care initiatives are complementary, not competitive with each other", Now, "leaving the specific details aside" assume a bit of a crowbar, he's at least headed in the right direction. While the expansion of Medicaid and Federerally Qualified Health Centers represents a significant expansion of government-provisioned health care, the bulk of the Affordable Care Act's goals are accomplished by making the dysfunctional individual health insurance market somewhat functional. Paul Ryan's Medicare proposal is to essentialy put senior citizens out onto the individual market.
The primary difference between the two, then, is what happens if costs continue to grow as they have over the past half-century. The Ryan plan pushes that cost growth onto individuals, and expects that seniors will be able to make rational cost-benefit decisions about their health in order to keep costs down. But this approach has its limits. In order to meet his budget targets, Paul Ryan had to both assume the creation of a large market for unicorn spotters to bring employment down to 2.8% and make the used-to-be-Medicare voucher quite stingy. The CBO estimates that the voucher will cover a mere 32% of health care costs. By comparison, Medicare currently has an actuarial value of 47.5%, and a Bronze plan under the ACA must have an actuarial of at least 60%. The results for individual seniors will be predictable. As Brad DeLong points out, under the Ryan Plan the vast majority of senior citizens will spend the majority of their income on health care.
The Obama alternative, rather than rely on individuals in their twilight years to make tradeoffs that result in lower cost at the risk of a shorter lifespan, is to push the cost growth onto the government books, and rely on the fact that once "health care" is universal, there will be more political buy in to make changes to the basket of goods and services that one can buy with your "health care", or to push providers to engage in delivery system reforms that will emphasize wellness over acute care. It's much easier for the government to make small tweaks -- reduce payments for this procedure by a few percentage points, stop paying for that test, reduce cancer screening from once a year to once per 18 months, etc. -- than it is for individuals to hunt for a plan that exactly fits their health care needs.