There are lots of different applications for analytics and a lot of ways to go about analyzing video. Some do simple pixel movement/differentiation, some do pattern analysis, some are manually calibrated, some are self-learning. There are still many platforms that downsample video to CIF resolution, and a few that can process higher resolutions (up to 720p or 1080p).
I'm not aware of any camera-side analytics that operate on a full uncompressed stream (based on the way the "image" is created in the camera, that would be hard to do). But camera-side processing *can* have the advantage of more control over the stream. If, for example, the camera was built with analytics in mind, the analytics engine could theoretically have access to a dedicated internal "stream", which can be adjusted based on the scene (scale resolution up or down, change compression aspects, and so forth) so that the analytics are not dependant on the parameters of stream optimized for bandwidth or storage or whatever.
Analyzing live video to detect objects of interest can be somewhat computationally intensive. Given "Moore's Law", it's practical to have a processor embedded in the camera that can handle this process at the edge. You eliminate network issues, and various contentions on a PC (OS issues, resource limitations) by running the analytics within the camera.
There are also hybrid approaches, where objects are detected in-camera, and then meta-data is streamed back to a server to handle the "rules" part of the problem.
Having analytics on the camera does not make them "more accurate", but it will *typically* indicate a slightly more refined or advanced system. You may be relatively limited in terms of camera choices, but the software is probably slightly more optimized to the hardware. Still, there are some PC-based analytics that beat some camera-based analytics, so none of this is an absolute.
This is a little bit like asking "Is all wheel drive better than 4 wheel drive", the reality is that there can be a LOT of minor distinctions that change what means "best" to you. What's really important is "Do you get the desired results within your budget?".
If you're evaluating analytics options, I would encourage you to look at both types. Pay attention to setup/calibration time (initially and ongoing), ease of tweaking/tuning the system over time, and coverage area/distance per camera (this can be a big one, I've seen some $50 solutions that cover 1/10th the range of a $200 solution, but look cheap on paper)