These digital payment services are different beasts that cater to different needs. Both provide a secure way to shop, with policies that refund your money in case of fraud. Here are some brief on both these services
Whats is Google Checkout ?
Google Checkout simply serves as a holding place for your credit or debit card information. It allows you to log in to a single Google username to shop, while hiding your valuable data and e-mail address from merchants. Payments could be made easily online.
What is Ebay's Paypal ?
PayPal's fine print is more complicated than Google Checkout's, but PayPal offers a wider variety of services for shoppers and businesses--particularly small ones--to exchange funds. Only PayPal lets shoppers transfer money to or from bank accounts in addition to credit and debit cards, and you can use it to wire money to other people without requiring them to get a paid account. PayPal is the only way to go if you're shopping around the world.
What are their limitations ?
Merchants with a U.S. address and bank account can process transactions through Google Checkout. Buyers with a U.S. billing and mailing address can make purchases through Google Checkout. In shoort Google Checkout is currently US only service.
PayPal caters to a wider range of audience, Its active in 55 plus countries, and already has a good customer base through out the world.