When I use the Burst feature for Burst shots using my Sony DSC H2 P&S the Image quality drops from 6 MP to around 2 MP.
That's interesting. I've owned a number of compact digital cameras and I've never had one reduce the MP in order to use Burst mode).
Is it a similar situation while using a DSLR?
No, not automatically. You can, of course, lower the megapixel count.
There is one qualification to this comment. Some cameras have special features such as Highlight Tone Priority on the XSi. When it was enabled, Burst mode didn't work correctly. It's one of those subtle things that took some time to figure out.
So if you enable certain settings, the effectiveness of Burst mode may be reduced. Simply turn off the feature and Burst mode will work fine.
Will The Image Quality drop while taking Burst shots of an action ?
No. But initially, images may be blurred until you get used to using Burst mode and some of the related settings, such as a Servo mode.
[edit] or can I get Burst shots at around 6 MP to 10 MP using these DSLRs[/edit]
Related reading: Servo modes (also known as Predictive Autofocus)http://www.digicamhelp.com/camera-logs/11/dslr-focus.phpSee above.