You can't compare Windows and Linux, because video driver performance and features are different. For instance, if you are using nVidia you need a card that supports vdpau for best performance, which is equivalent to PureVideo in Windows. PureVideo supports many more cards. However, depending on your CPU, you can play HD videos smoothly without vdpau support. So depends on your video driver, CPU and also player settings.
It would help if you could provide more info about your video card and CPU.
Anyway, try smplayer
Is the best player IMO and plays even videos with resultions higher than 1080p on my Core2 Duo with nVidia 7300 GT (not vdpau).
Make sure you tweak smplayer. In the preferences, click the "Performance" section and select the option "Skip only on HD videos" in the "Loop filter" settings. In the "General" section, click the "Video" tab and make sure the "Output" driver is set to "xv".