In its first official day trading as a public company, PayPal’s market value climbed to near $49 billion, eclipsing the market cap of its former parent company eBay.

Under pressure from activist investor Carl Icahn, eBay decided last fall to spin-off PayPal, the digital payments company it acquired more than a decade ago for $1.2 billion.

PayPal’s shares rose 5.4% to close at $40.47. eBay’s shares EBAY gained 2.4% to close at $28.57, giving the marketplace a $35 billion valuation.

The difference in public values of both companies reflects the divergent paths each company are on as they separate. PayPal continues to grow fast, as more consumers flock to the Web and to mobile devices to pay for what they buy. EBay has had a tougher time growing amid competition from e-commerce giants like Amazon AMZN .

In its earnings last week, eBay’s second quarter revenue fell 3% to $2.1 billion (revenue actually was up slightly, 5%, in the quarter excluding unfavorable currency fluctuations).

In contrast, PayPal saw revenue jump 16% to $2.3 billion, beating eBay’s marketplace sales for the second straight quarter. The value of transactions handled by PayPal was also up, growing 20% in the second quarter to $66 billion.

It’s worth noting that payments through eBay marketplaces is still significant for PayPal. In the second quarter, PayPal users spent $14.5 billion on eBay, representing 22% of PayPal’s total volume.

The big question is whether the two companies will play nice in the future. For now, eBay has promised that 80% of sales in the marketplace would continue to be routed through PayPal for the next five years. But eBay can also bring on additional payment providers if it chooses.

PayPal, as an independent company, is free from the shackles of eBay bureaucracy, which could be a positive thing for the company, explained Sucharita Mulpuru, analyst at Forrester Research. But the company will also be under more pressure to meet quarterly goals, she added.

And PayPal is not without competition. The company faces challenges from Apple Pay and Google’s Android Pay along with Silicon Valley upstart Stripe, which, behind the scenes, powers online payments for merchants.