The Center on Budget and Policy Priorities explains some aspects of the House health reform bill that lead to better coverage than the Senate Finance bill - the House bill would cover an estimated 96% of non-elderly uninsured, about 2% better than the Finance bill. The health insurers did have a point when they objected that the lower level of coverage in the Finance bill would lead to some growth in insurance premium costs; this objection would be more muted under the House bill.
In addition, the House bill does some things with Medicare payments that are better than the Finance bill. It's important to note that under any bill, no senior will have their benefits reduced from the statutory Medicare benefits. It's more correct to cast the Medicare Advantage cuts as eliminating unjustified subsidies to private companies rather than cutting Medicare.
Shared Responsibility Requirements for Individuals and Employers
The House bill includes a more robust requirement for individuals to have health insurance than the Finance Committee bill. The Finance Committee exempts households from the penalty that it would establish for not having coverage if they would have to pay more than 8 percent of their income for premiums. As a result, there is risk that under the Finance bill, significant numbers of people in good health would forgo coverage. That would cause the pool of people buying coverage through the exchange to be less healthy on average, and consequently would result in higher premiums and increased subsidy costs for the government. The House bill, in contrast, waives the penalty for not having coverage only for households that would experience a hardship based on their individual circumstances. Moreover, the House bill sets the penalty for not having coverage at 2.5 percent of adjusted gross income, considerably higher than the Finance Committee bill, which phases in the penalty to a maximum of $750 per adult in 2017. As a result, the House bill would likely cause many more individuals, particularly those who are healthier, to enroll in coverage rather than remain uninsured. 
The House bill also includes a stronger, simpler requirement on employers to offer health coverage than the troubling provision in the Finance Committee bill. Under the House bill, employers must either offer coverage meeting certain standards or pay a fee equal to a percentage of their payroll. (Most small employers would be exempt from this requirement.) This provision, along with the requirement for individuals to have coverage, is the reason why CBO estimates that the House bill would increase the number of people enrolled in employer-sponsored insurance in 2019 by 6 million, relative to current law.
In contrast, the Finance Committee bill would modestly reduce employer-sponsored insurance, by 3 million. Its employer responsibility requirement would penalize only those firms whose workers receive premium tax credits through the new health insurance exchange, whether employers offer coverage or not. This would give employers an incentive not to hire workers whose family incomes are low enough to qualify them for premium credits.
Making Medicare More Efficient and Slowing the Growth in Health Care Costs
The House bill includes a number of provisions that would make Medicare more efficient, which would help slow the growth in health care costs as well as help pay for health reform and desirable beneficiary improvements to Medicare (including improvements to the Medicare drug benefit and making more low-income Medicare beneficiaries eligible for help with their premiums, deductibles and co-payments). Many of these provisions are in line with the recommendations of the Medicare Payment Advisory Commission (MedPAC), Congress’ expert nonpartisan advisory body on Medicare payment policy, on how to modify provider payment rates and encourage efficiency while ensuring that payments are adequate so that beneficiaries continue to have access to health care providers.
Elimination of Medicare Advantage Overpayments
One key provision in the House bill, which MedPAC has long recommended, would eliminate the overpayments that private insurers receive through the Medicare Advantage program. Even though private plans were brought into Medicare to lower costs, it currently costs the federal government 14 percent more on average, or over $1,100 more per person, to cover the same beneficiaries through private plans than through traditional Medicare. These overpayments drive up beneficiary premiums and advance the date when the Medicare Hospital Insurance Trust Fund is projected to become insolvent by 17 months. While the Finance Committee bill significantly scales back these overpayments (thereby saving nearly $120 billion over ten years), the House bill would phase these overpayments out altogether over three years, as MedPAC has recommended. Along with other Medicare Advantage savings in the House bill, eliminating the overpayments would lower Medicare spending by $170 billion over ten years.
Reductions in Medicare Drug Costs
In addition, the House bill would lower the cost of prescription drugs in Medicare. Prior to the establishment of the Medicare Part D drug benefit, Medicaid provided prescription drug coverage to more than 6 million “dual eligibles” (low-income Medicare beneficiaries who also are enrolled in Medicaid). In 2006, drug coverage for these dual eligibles shifted to Medicare. When Congress created the drug benefit, it assumed that the private insurers participating in Part D would be able to negotiate larger rebates from drug manufacturers than Medicaid had required. But an increasing body of research demonstrates that the rebates negotiated by Part D plans are well below the Medicaid rebates, which means the federal government is incurring significantly higher drug costs for dual eligibles than it previously incurred under Medicaid.
The House bill addresses this problem by requiring drug manufacturers to provide, at a minimum, the same rebates for drugs provided to dual eligibles under Medicare Part D as Medicaid would require. The bill would devote some of the savings from this provision to filling the so-called “doughnut hole” in the Part D drug benefit. Even after financing this improvement to the Medicare drug benefit, CBO estimates that this provision of the House bill would still produce net savings of $42 billion over ten years to help pay for health reform. The Finance Committee bill does not include this provision (or the closing of the doughnut hole in the drug benefit).
Other Medicare Reforms
In addition to instituting cost efficiencies in Medicare, the House bill (like the Finance Committee bill) takes important steps toward restructuring Medicare’s payment system to promote effective, high-value health care. It reduces Medicare payments to hospitals with high readmission rates to encourage them to do a better job of preventing avoidable readmissions. It creates an alternative payment model to reward Accountable Care Organizations — physician-led organizations that take responsibility for the cost and quality of the care they deliver. It expands efforts to assess the feasibility of paying for qualified patient-centered medical homes and of bundling payments for hospitals and post-acute providers. To the extent that these approaches prove successful, the bill would require the Secretary of Health and Human Services to implement them on a larger scale. The bill also contains numerous provisions to improve program integrity and reduce fraudulent payments in both Medicare and Medicaid. Because Medicare has served in the past as a leader in developing and testing effective payment reforms that are later adopted widely by private insurers, these reforms have the potential to slow health care growth not only in Medicare but throughout the U.S. health care system.