Often this is not the case, especially for low end cards.
The performance of video playback is largely dependent on the video accelerators present.
Let's say you want to buy a dirt cheap GeForce 8400 GS. Take a look at the specifications:
NVIDIA® PureVideo™ HD Technology: The combination of high-definition
video decode acceleration and post-processing that delivers
unprecedented picture clarity, smooth video, accurate color, and
precise image scaling for movies and video. Feature requires supported
video software. Features may vary by product.
Discrete, Programmable Video Processor: NVIDIA PureVideo is a discrete
programmable processing core in NVIDIA GPUs that provides superb
picture quality and ultra-smooth movies with low CPU utilization and
Hardware Decode Acceleration: Provides ultra-smooth playback of H.264,
VC-1, WMV and MPEG-2 HD and SD movies.
HDCP Capable: Designed to meet the output protection management (HDCP)
and security specifications of the Blu-ray Disc and HD DVD formats,
allowing the playback of encrypted movie content on PCs when connected
to HDCP-compliant displays. Requires other HDCP-compatible components.
Spatial-Temporal De-Interlacing: Sharpens HD and standard definition
interlaced content on progressive displays, delivering a crisp, clear
picture that rivals high-end home-theater systems.
High-Quality Scaling: Enlarges lower resolution movies and videos to
HDTV resolutions, up to 1080i, while maintaining a clear, clean image.
Also provides downscaling of videos, including high-definition, while
preserving image detail.
Inverse Telecine (3:2 & 2:2 Pulldown Correction): Recovers original
film images from films-converted-to-video, providing more accurate
movie playback and superior picture quality.
Bad Edit Correction: When videos are edited after they have been
converted from 24 to 25 or 30 frames, the edits can disrupt the normal
3:2 or 2:2 pulldown cadence. PureVideo uses advanced processing
techniques to detect poor edits, recover the original content, and
display perfect picture detail frame after frame for smooth, natural
Noise Reduction: Improves movie image quality by removing unwanted
Edge Enhancement: Sharpens movie images by providing higher contrast
around lines and objects.
This card may support higher resolutions, but can only play back videos of the later formats (which covers most of the ones you want) at 1080p.