How are you shooting? Are you shooting in RAW? If not, you need to do so. Shooting in Jpeg, especially if you are shooting at one of the lower resolution settings, means you are a slave to however the camera wants to render the photo. By the way, if you are shooting in Jpeg, unless you change it in the menu, the camera does NOT automatically shoot at it's highest quality / highest resolution.
When shooting in RAW, you then convert the files into a Jpeg or Tiff in the RAW converter. The Canon software, Digital Photo Professional, is on a CD that came with your camera. It is an "ok" program and will allow you to adjust the RAW photo as pertains to sharpness, color, contrast, exposure etc. As it is free, it's a good place to start, but there are better programs out there. My personal favorite RAW conversion software is "Capture One".
At any rate, it sounds as if you are just not taking enough control of your photos. Using a 35mm lens on a full frame camera means depth of field should not be too big an issue, though if you are shooting at large apertures such as 1.8, then you most likely WILL have depth of field problems, especially since you say the subject is sharp. Try taking photos at smaller apertures such as f8 and see what results you get.
If you want the ENTIRE SCENE sharp, you have to use a smaller aperture which can mean a slower shutter speed which in turn can mean you will need the camera on a tripod.
I'm not sure what you mean by "crisp", and I also have no experience with a Sigma lens, but I do not believe the lens is your problem.
Again, shoot in RAW and learn to process your photos to be their best, and try shooting at smaller, (higher fstop) numbers to see if lack of depth of field is taking away your "crispness".
A final note, a full frame camera will have LESS depth of field than a crop sensor camera so if you have moved from a crop sensor camera to a full frame, the DOF is not going to look the same between the two cameras at any given aperture. You have to stop down the aperture on the full frame camera to get the same depth of field you have on a crop sensor body.