On the technical side, people always talk about old rat vs. new rat, but there are actually three rats: the original rat, the USA rat-2, and the Chinese rat-2. (Read on - there are actually 5.)
Most people know about the original vs. rat-2 discussion. There were minor changes to the actual circuit when the rat-2 was released (which is probably why they renamed it). But what many don't know is that when they moved production of the rat-2 to China, they reverted to the original rat circuit.
The original to rat-2 changes in 1988 were partly minor changes to the actual audio circuit, but mostly the addition of a true bypass capable LED indicator circuit. A new PCB was introduced for this, which was also capable of implementing the orginal rat circuit. The last issues of the small-box black-face original rat used this PCB, as well as the rat-2 and turbo-rat. Over time, other rat models were released, and therefore production changes occurred. Jumping ahead to 2002,
the deucetone rat was released, and it featured a 3PDT footswitch (by then plentiful and cost-effective) to handle the indicator LED, thereby eliminating the need for that portion of the rat-2 circuit changes. The deucetone required a new PCB to allow the position of the footswitches to be at the sides of the PCB (as well as the center), and this PCB was designed using the original rat circuit. It is easily identifiable by the three large holes for a footswitch. This PCB was eventually carried over into production of all other rat models including the USA rat-2, turbo rat, and the 2004
you dirty rat.
Side note: There was another PCB that was introduced in 1995 and was capable of implementing either the original rat, the rat-2 or
the turbo rat circuit (slight difference from rat-2, not just the clipping diodes). It was called the Multi-RAT and was used in all production models at that time - the rat-2, turbo rat, and the vintage rat big-box reissue. Note that this PCB did not introduce any circuit changes, it just simplified the production process.
When production of the rat-2 moved to China, the same 3PDT switching and original rat circuit was used. Note that it has been reported that the filter control cap is a slightly different value than the original, so it isn't identical, but that is arguably not a sonic difference only a difference in the range of the filter control.
Keep in mind that the other big technical change happening is the op-amp change from an LM308 to an OP07, which started towards the end of USA rat-2 production resulting in two or three different USA rat-2s - probably three since it appears that the LM308 op-amp was used in the early days of the new PCB - the switch to the OP07 appears to have started sometime in 2003 or early 2004.
If you're still following, this means that apart from the op-amp, the Chinese rat-2 is more like the original rat than the early USA rat-2. It also means that there are probably a small number of USA rat-2s with the new PCB and an LM308, making them actually pretty much identical to the original rat circuit-wise.
So, the old rat vs. new rat discussion is rather complicated. This could explain why some people do a comparison and hear little difference, and others hear a big difference.