In general, to take online payments, there are two classes
of solutions:
1. get your own merchant bank account
2. use a "third party payer"

There are different kinds of merchant bank accounts; the exact rates
possible are dependent on the kind of organization, whether it is
MOTO (mail order telephone
order -- the class for internet) or brick and mortar ("card in hand"),
and other factors. The process is the same to get a merchant bank
account for online payment, as it is to get a physical "card swiper"
for a store.

With a merchant bank account, you have total control over the user's
experience on your web site. The user never has to leave your web
site, and you can tailor the form in any manner you please.
The funds go from the user's bank account directly into your
merchant bank account.

Applying for a merchant bank account can take several weeks, and
integrating the interface to the payment gateway requires the
help of a software developer.

The "third party payer" solution relieves you of the bother of getting
your own merchant bank account. The payer uses their account, and then
distributes to your later on. This is called "factoring" and is in a
grey area legally in the U.S., but so far it has not been cracked down on
except for areas as online gambling.

With such a solution, the user always leaves your web site to make 
the donation, and goes to the third party payers. You never see the
credit card data yourself. You have some limited customization ability
over the form that is hosted for you on the other site.

Paypal and GroundSpring are both "third party payer" solutions.
They offer similar rates: groundspring is 3% of each transaction,
plus $14.95/month.
Paypal is 2.9% + $.30 for each credit card transaction, with no monthly
charge. (Paypal offers lower credit card rates for "qualified" accounts,
but qualification is not much easier than getting a direct merchant
bank account.)
By way of comparison, the transaction cost of a direct merchant
bank account is roughly %2.25 + $.25/transaction, + $15/month.
So the rates are all kind of similar.

Paypal differs from other "third party payers" in that in addition
to offering credit card payments, they also support "person to
person" payment, if the user has set up to be a paypal member.
Paypal makes money on this "person to person" payment system,
which is one reason that the usability of the paypal web site
is deliberately hampered.
With groundspring, it is possible to have just one web form, and
the user goes in and out. This is more difficult with paypal, which
has a more confusing layout, and supports less customization
of look and feel.

My experience with paypal is that it works out fine if your
users are already paypal members, or are technically savvy.
If the donors are not technically savvy, paypal does not work
well. They get confused.

Note that groundspring will only work with nonprofits.
They say they will work with international charities, not
just US-registered 501c3s, but I don't know what their criteria
are out of the U.S.

Another important factor is support. By the nature of the size
of their user base, support from paypal is not satisfactory, so
when there are problems, it is much easier to go to a smaller
more dedicated company like groundspring.