Both side-focus and an adjustable objective essentially correct the focus of the reticle, but the side-focus does it inside the scope, rather than by moving the objective lens. Generally an adjustable objective is considered more precise and perhaps tougher, but side-focus is certainly handier--at least for right-handed shooters!
I don't know why a side-focus scope would be dimmer than an adjustable-objective scope, and haven't noticed it in using a number of side-focus scopes. Is the reticle in your older scope a plain plex-type, and the reticle in the new scope a "ballistic" type? Usually plain plexes are wire, while ballistic reticles are etched. The glass that reticles are etched on is usually uncoated, and can slightly dim the image, though the difference normally isn't vast.
