It depends!
Some motherboards (you'll find info on them at
http://go.to/geforcefaq ) have an inherent weakness.
One problem can be the maximum power (limited on some) while the other can be an AGP 1.0 port with only 2x speed and 3.3v power - and although boards and slots are keyed (or SHOULD be) to prevent incompatible voltage insertion, there can be other compatibility issues.
My Geforce 2MX SAYS it want's an AGP 2.0 compliant system, but runs fine in the AGP 1.0 slot - not sure how far up the Nvidia range this level of compatibility extends.
Most of the ATI cards are 3.3v and AGP 1.0 tolerant, and if it's one that uses a drive connector for power, it gets around any slot power limitations.
http://www.ati.com/support/faq/agpchart.html
The "universal" voltage cards are capaple of 3.3v (AGP 1.0) and 1.5v (AGP 2.0) voltages, but only "MAY" be compatible with AGP 1.0 systems.
(extract)
RAGE 128 PRO, RADEON, and newer products are keyed “Universal AGP” and may operate in AGP 1.0 and AGP 2.0 compliant motherboards. Please check with your motherboard manufacturer if you are uncertain about the AGP specification it meets.
The Nvidias also seem to be dual voltage throughout the range, so it's possible it may work.... - again, drive-connector powering would be reassuring on the AGP slot power conditions.
One issue was that some older AT/ATX dual powered motherboards powered the 3.3v AGP with a liner regulator of limited power - a kludge on some if running with ATX power was to disconnect the regulator and hardwire the AGP power direct to 3.3v from the ATX PSU.
The other method of powering the slot - and the method used by cards which take a drive connector, is a switchmode regulator from the 12v - though this can expose a rather low 12v rail amperage on cheaper PSUs, as this is also used (switchmode regulated) to power the CPU, as well as every fan and drive motor in the system!