You have to remember that lens resolution is not a single number. It's an MTF curve describing detail contrast for a given resolution. The higher the resolution, the lower the detail contrast. For a given number of megapixels, crop sensors use smaller pixels. That means detail is recorded at a lower point on the lens MTF curve...lower contrast...vs. a FF sensor.
So yes, FF DSLRs provide sharper images out of camera.
However, at low to mid ISO this is a non issue. All DSLR images (or at least all DSLR images with AA filters) benefit from sharpening, and most benefit from local contrast enhancement. You're going to sharpen the files either way. With crop you just sharpen more in your RAW converter or PS. If you want out of camera JPEGs, you turn up the camera sharpening a little more.
At high ISO this works against crop bodies because the sharpening enhances the noise. And it's at high ISO that I think FF really distinguishes itself. But for all the talk about FF vs. crop, at low to mid ISO there really isn't much difference. Nothing that would stand out even in a 24" print. (Even 4/3rds is capable of matching crop/FF with the same MP count at low ISO.)
Diffraction softens the image. At f/22 (FF) and f/16 (crop) the impact is enough that you cannot fully compensate with sharpening in post. I do not use f/22 on FF, and do not use f/16 on crop, except in very special circumstances. With landscape shots I try to use hyperfocal focusing and the largest aperture possible while still retaining the DoF I want. LiveView is great for evaluating this.
Note that diffraction does not impact any format more than any other for a given FoV and DoF.