In 1997, the second generation YZF600 was produced which brought in major changes to the styling and some advancements in the suspension. In the rest of the world, the FZR600 was finally dead and the only 600 supersport offering by Yamaha was the YZF600. This model is also known as the "Thundercat".
Mechanically, the two bike are so close to being identical you have to really know what to look for to find the differences (besides cosmetic ones).
The Changes:
Besides cosmetics, the only external change was the addition to fully adjustable front forks. Most of the other changes involve the engine. The charging rotor was changed to adjust timing. This was done to aid in the addition of a RAM AIR intake and a Throttle Position Senor (TPS) so that the TCI computer could alter timing based on throttle and speed.
What this means for you:
Basically, you need to pay attention to which model engine you are dealing with. This is especially true if you are swapping engines around for a hybrid build. The TCI computer from the 97+ will not run the 95-96 engine for very long and viceversa. One of the main issues when converting to a 97+ YZF engine is dealing with the RAM AIR system. If you ever wondered why the YZF600 was so big, just look at the plumbing for the RAM AIR. The fairings needed to be large to hide all of it. Unfortunately, removing this system usually results in lower performance. But there are ways around this. You can run a 97+ YZF engine without the RAM AIR and not have the draw backs by using the 95-96 YZF600R air box or a modified FZR400 air box. But, both of these model engines are direct bolt in to the FZR600 and FZR400 chassis. Granted you will have to deal with sprocket alignment and radiator mounting issues and you will need the complete wire harness and TCI. If you are needing to get a new engine for you Foxeye or Thundercat, you can just swap and go.
The Big Picture:
The YZF600 had a long life just like the FZR600 did. It was in production for 13 years in one form or another with 07 being it's final production year. Parts are easy to come by if you need to fix something or you are looking to upgrade you Fizzer. And Yamaha made a lot of things easy for use by using similar castings for so many years meaning you can swap parts between bikes with ease.
Good Luck!