Welcome to the forum.
There could be a few issues here. Firstly, most small digi-cams have the settings cranked up by default, so the images often look more 'finished' when right out of the camera. DSLR cameras might do less tweaking to the images, giving the photographer the chance to make their own choices.
Also, I think that DSLR cameras are more prone to camera shake blur because the focal lengths are longer than that of small digi-cams. So when the light isn't great (indoors) you need to watch your shutter speed...and if it's too low, you need to compensate in some way, maybe use a support or maybe turn up the ISO.
97% of the time, issues like this are the result of user error or a lack of information / understanding.
To really diagnose the problem, it would help if you could post some examples, along with the EXIF info (shutter speed, aperture, ISO etc)