It really does depend a lot on the operating system. I never could see much of a difference in 2D speed under Windows 98. Even at relatively high resolutions like 1600x1200 modern PCI cards are nice and quick under Win98.
XP is a different story. At 1024x768, you can see a slight difference in 2D speed between PCI and AGP (I tested this with a Radeon 9250 PCI and 9800 Pro AGP on a 2.66GHz P4 system). Bump the resolution up to 1920x1200 and the difference between PCI and AGP is like night and day. For example, when you reload a web page, you can see the PCI card refresh the screen from top to bottom. With AGP, it all appears on-screen at the same time.
So at least under WinXP, high resolution 2D really does suffer. I found that reducing the color depth to 16-bit helped the PCI card immensely, but it was still visibly slower than AGP.
Now, if you really wanna see some slow 2D, try running running Win7 at 2560x1440 on a PCI card. I tried that with a Radeon X1550 PCI on a 3.33GHz Core 2 Quad system. Despite the quick CPU, performance was very much in the crapper--it couldn't even handle plain old DVD smoothly. Even simple stuff like window drags were choppy. The C2Q board was designed for PCIe video cards, so its plain old PCI performance may have been a bit lower than that of an older system.
P6 chip. Triple the speed of the Pentium.
Tualatin: PIII-S @ 1628 MHz | QDI Advance 12T | 2GB DDR-310 | 6800GT | X-Fi | 500GB HDD | 3DMark01: 14,059
Dothan: PM @ 2720 MHz | MSI Speedster FA4 | 2GB DDR2-544 | GTX-280 | X-Fi | 500GB SSD | 3DMark01: 42,148