They are all the "Best Ones" and they are all the worst too. Each has it's strong points and weak ones.
The big knocks against the 1st gens (from wimps mostly) were that:
It would allow the rider to feel some of the higher power that it puts out as heat on the rider's legs. Easily rectified with a few home-made-mods.
A relatively small population had problems with the valve stem seals wearing prematurely, resulting in guide wear, and what is known as a "ticker".
The 2nd generation added a few "features" like improved air management that results in less engine heat being felt by the rider.
Also improved the engine's valve guide seals and guides (which can be put into the 1st gens during a top end rebuild) to prevent tickers. There are no known ticker 2nd gens.
The knocks against the 2nd gens are:
They redesigned everything to accommodate the YCCS (auto clutching version).
In this redesign they screwed the pooch on a number of things:
The throttle cam rate changed resulting in a throttle that is hard to control.
They messed up the ECU fuel injection firmware resulting in a problem if the bike was ridden at varying altitudes (recalled)
The clutch rate became grabby and stiffer because of the ratio required for the YCCS. (fixed in later 2nd gens after they ditched the YCCS)
They built an all new electrical wiring harness for the 2nd gens, which routed too much current through the ignition switches causing them to sometimes meltdown (recalled)
And they added the ground block "spiders", which also have excessive current routed through them (also recalled). Both of these will put you dead on the road, out in BFE.
The bike is heavier, for no apparent reason.
The bike is longer in wheelbase, which is generally not considered a great thing for quick handling.
The front forks were redesigned for no apparent reason and now the bushings wear out earlier.
I ride a 1st gen (can you tell?) Would I ride a second gen if there were no 1st gens? Farking right I would. But as long as there are first gen FJRs available with low mileage at decent prices, that's what I'll have.
The 2nd Gen FJR is the 2nd best bike Yamaha has ever made.