What is better, Average speed or long distance? I am rebuilding my bike fitness and was wondering the effects of slow long distance training vs maintaining a decent average speed.

What difference it makes if i choose one of the above?
It depends what sort of bike fitness you are trying to build, your current level, and your riding history.

I'd start by saying that simply trying to maintain a high average speed is a poor training method for anything, and I think you'd struggle to find a coach that advocated such training.  It simply produces fatigue without actually going hard enough to produce significant training stimulus. 

Long slow distance (LSD) will predominantly build your endurance and your ability to burn fat as fuel rather than carbohydrate.  If you are targeting long distance rides then these are an ideal starting point.

If you are more interested in shorter events like 90 minute criteriums/XC mtb then building a large endurance engine is not so valuable, and you are better off targeting short hard efforts (2x20's, 5x5's, 30/30s etc) to build your speed.

For most people, a combination of both is going to be best to become a strong all round cyclist.  There are any number of 'sportive' training plans on the web that will help with this.  British cycling have a range of Training Plans for beginner to advanced that are free to download.