PayPal (PYPL - Get Report) is on the rise, and Amazon (AMZN - Get Report) is slipping in one key category according to new research. 

Among top Internet retailers, eight more added PayPal as a form of payment last quarter, wrote Morgan Stanley analyst James Faucette in a note to clients on Thursday. Amazon Pay declined in merchant acceptance in the same period, losing four top 500 retailers, while Bitcoin acceptance remained flat. 

That means PayPal is accepted as a form of payment at 82% of top retailers, according to Faucette, while Amazon Pay is accepted at just 4% of non-Amazon retailers. Bitcoin was accepted at just over of the top 500 retailers. 

"We think its acceptance lead vs. other digital wallets and consumers' shift toward online purchases should support PayPal's TPV [third party vendor] growth at or above the rate of eCommerce," Faucette wrote. Morgan Stanley raised its target price for PayPal to $99 from $97.

PayPal shares were roughly flat on Thursday, and closed at $90.40. 

So how does one explain Amazon's relatively abysmal acceptance rate? Zev Fima, an analyst with Jim Cramer's Action Alerts Plus portfolio, broke down why many non-Amazon sellers aren't as motivated to use Amazon's payment system.

"The dynamic, PayPal gaining and Amazon losing in the online payments space, does not come as a surprise because, as we told members a May 2018 trade alert, we find it highly unlikely that retailers will want to partner with Amazon, their direct competitor," Fima said. "This makes any exodus from PayPal's system to Amazon Pay likely minimal in size. After all, Amazon is the traditional retail industry's biggest rival."

PayPal is due to report earnings on Jan. 30 after market close.  

Amazon and PayPal are holdings in Jim Cramer's Action Alerts PLUS Charitable Trust Portfolio. Want to be alerted before Cramer buys or sells these stocks? Learn more now.