ResMed Inc (ASX: RMD) and Cochlear Ltd (ASX: COH) are two of Australia's most successful global healthcare shares.
Both have established themselves as leaders in their respective markets, helping millions of people improve their quality of life.
And I believe both have considerable opportunities to grow over the coming decades. But if I could only buy one of these ASX healthcare shares today, which would I choose?

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ResMed shares
I think ResMed is one of the highest-quality healthcare shares on the ASX.
The company is a global leader in sleep and breathing health, best known for its devices for treating obstructive sleep apnoea.
And its recent financial performance has reinforced my confidence in its long-term prospects.
Last week, ResMed released its first-quarter results, reporting a 6% increase in revenue to US$1.41 billion, driven by continued demand for its products.
Global sleep device revenue increased 9%, while masks and other products grew 10%.
There was also good news on profitability, with adjusted earnings per share (EPS) increasing 14%.
I like that ResMed is managing to grow earnings faster than revenue, helped by improvements in manufacturing efficiency and gross margins.
Management also maintained its FY27 guidance, which includes core constant currency revenue growth of 5% to 7%.
Looking further ahead, I believe there is still a substantial opportunity for growth.
Millions of people around the world are living with undiagnosed or untreated sleep apnoea. As awareness improves and more people gain access to treatment, ResMed should be well placed to benefit.
And with the company continuing to invest in new products and technology, I think it has an excellent chance of becoming considerably larger over the next decade.
Cochlear shares
Cochlear is another healthcare business I rate highly. The company is a global leader in hearing implants, with its technology helping people with severe hearing loss hear again.
And despite its established position, the long-term growth opportunity remains enormous.
According to Cochlear, fewer than 5% of people who could benefit from an implantable hearing solution have received one. That's a significant figure and demonstrates how much potential demand remains untapped.
Cochlear is working to address this through greater awareness, improved referral pathways, and continued product innovation.
Its recently launched Nucleus Nexa System is an important development, while its research into fully implantable hearing technology could create additional opportunities.
However, the company's recent financial performance has been disappointing. In FY26, underlying net profit declined 22% to $322 million, reflecting softer implant demand, lower margins, and higher costs.
Management expects some improvement in FY27, forecasting underlying net profit of between $330 million and $350 million. That's encouraging, but I think Cochlear still has work to do to restore stronger earnings growth.
Its long-term opportunity remains attractive, although investors may need to be patient as the business works through its current challenges.
Which would I buy?
For me, ResMed has the edge when it comes to both earnings growth and valuation.
At recent share prices, ResMed is trading on a price-to-earnings (PE) ratio of approximately 20 times consensus FY27 earnings according to CommSec.
Cochlear, meanwhile, trades at approximately 27 times earnings, based on the midpoint of its FY27 underlying profit guidance.
I think the valuation gap is significant, especially given how the two businesses are performing.
ResMed's latest results showed strong demand for its products and improving profitability, with adjusted earnings per share increasing 14%.
Cochlear, meanwhile, is still working towards an earnings recovery following a challenging FY26.
I believe Cochlear has enormous long-term growth potential, and its earnings could strengthen considerably over the coming years. However, with ResMed delivering stronger results while trading on a lower earnings multiple, I think it offers the better buying opportunity today.
Foolish takeaway
I would be happy to own both ResMed and Cochlear for the long term, but ResMed shares would get my money today.
I believe its combination of established market leadership, growing earnings, and a reasonable valuation makes it a compelling investment.
Cochlear remains a business I admire, and I think its growth prospects could eventually justify a stronger share price.
For now, though, ResMed is my preferred ASX healthcare share to buy and hold.