One of the reasons I don't do counted cross-stitch is because there is limited texture. The images are based on color differences following a grid and using usually only cross-stitch to fill and backstitch to outline. Boring.....
The piece here, "Brave", uses a combination of French knots and whipped running stitch in the red areas, covering the background with a pattern that allows the fabric to show through, and my "signature stitch" in the purple areas- a random cross-stitch which is great for color blending and dense coverage. This piece started with a printed fabric which I used for a more spontaneous way of working- responding to the existing pattern and colors rather than planning everything out ahead of time. This is sort of what my current stitch students are doing. We created a collaborative print and now they are responding to it. I'll get pics up when they're complete.
In freehand embroidery, one is not limited by the grid and you can create a much more dimensional and textured surface. Try building up areas of mark and color by stitching the same type of stitch densely over an area of fabric. Think of stitches as marks as important as brushstrokes in a painting or hatchmarks in a drawing.
Some artists play with density and allow the background fabric to play a part in the design. Check out Karin Birch's work: http://karinbirch.blogspot.com/ Here is her piece, "The Marriage". Her stitching echoes what is on the surface. Some areas are densely stitched or beaded, others use more line-drawing type stitches to allow the background to come through.
Karin Birch shows her work at Snyderman Gallery in Philadelphia and it's worth stopping by to see it if you're in Old City.
It's possible to completely cover your background fabric with stitched texture. Take a look at the work of Renie Breskin Adams on this link:
OF course, the more stitching, the longer it takes to complete. This is why I've developed ways of printing or painting on my background fabrics, or using a variety of appliqued fabrics so that I can make more pieces and not kill myself working on a single image for months on end.