Linear Rate - also known as straight rate or constant rate springs, are were the entire spring is wound at the same pitch, therefore every kg of force has the same effect on the spring throughout its length. For example, if it takes 25kg of force to compress the spring one inch it will take another 25kg (50kg in total) to compress it the second inch and so on until the end of the travel.

Progressive Rate - are wound progressively from a finer pitch at one end to a coarser pitch at the other, therefore having a rising rate resistance to compression. For example, a 15kg to 25kg progressive spring rate will take 15kg of force to compress the spring one inch, then an additional 17kg of force the next inch and so on until the end of the travel, the last inch takes an additional 25kg to compress it .

The Evidence -

The pro progressive spring people will advocate that you are getting the best of both worlds, you'll be getting a spring that can be soft enough at the start of travel to absorb small road bumps and provide a more 'comfortable' ride, yet still offering the firmness at the end of the travel to handle the big bumps and potholes, major loading under braking and preventing bottoming out. Progressive fork springs are very popular with cruisers and sportstourers.

So why then do the pro linear rate people always say that straight rate springs are better? What's the problem with progressive rate springs?
The first problem is that sportsbikes and racing bikes simply do not have enough suspension travel to take advantage of the progressive rates. The initial softer part of the spring just gets used up straight away leaving a limited amount of travel for the stiffer portion to deal with, resulting in less compliance and less traction. The second problem is that damping rates need to be matched to the spring rates, inparticular rebound damping, with progressive rate springs this is impossible. Damping is always a bit of a compromise and adding progressive springs to the mix just makes the job so much more difficult.

The Conclusion -

For sportsbikes and racing bikes virtually all suspension tuners will recommend linear springs, but if you have cruiser or tourer then progressive springs may be the perfect option.

So which are actually best was the original question. You really need to make your own judgement based on your type of bike and what you want from the suspension. This article is only a guide to help you make an informed decision, there is no definative answer!!