Mallinckrodt's stock rose 6.8 percent to $64.84 per share, while Mylan's stock rose 2.29 percent to trade at $43.69 per share.
Mylan CEO Heather Bresch said the company has differentiated itself from the competition with its investments in manufacturing and research and development, as well as strategic acquisitions such as its bid for Swedish drugmaker Meda Aktiebolag.
"We believe we have an operational platform that has over 1,500 products – over 2,000 with Meda. We've got a commercial footprint across the geographies that's truly second to none," she said in an interview with CNBC's "Closing Bell" Tuesday.
"There's huge differences between that and slashing cost, slashing R&D, slashing jobs and raising prices," she said.
Guggenheim Partners analysts Louise Chen and Brandon Folkes weighed in on both stocks Tuesday. Chen and Folkes wrote they were confident that Mallinckrodt will meet or beat earnings expectations for the fiscal year. But they were more neutral on Mylan, waiting on the sidelines to see the results of a merger with Meda and the sales of EpiPen and generic Advair.
Still, not everyone is bullish on Mallinckrodt's prospects. The company has been the target of a high-profile battle with short seller Andrew Left, and the stock has declined 43.45 percent in the past year.
—CNBC's Peter Schacknow contributed to this report.