You will 100% notice a difference in sharpness and AF performance, both in low light and continuous focus (tracking).
Noise, though, won't be very noticeable unless to a trained eye - the K-5 is incredible in its noise prevention, and the K-3 will inherently have the appearance of having more noise when viewed at 100% (i.e. pixel peeping) on your screen because the resolution is much higher, making the grain appear 'more.' But after resizing down, the noise is finer (because of the higher resolution) and will seem like its less. But in the end it's pretty identical, which is in itself pretty remarkabl considering the difference between 16 and 24 mpx.
In short, don't buy the K-3 over the K-5 for pure noise benefits. But if you are interested in autofocus, both in near darkness and tracking, and total resolution, the K-3 will trounce the K-5. A great camera, but overall the K-5 is no match for a K-3 (for many, many, many other reasons than the two quickly mentioned).
If I were you, considering similar price points (about $1000-1200 for the K-3 or the DA* 60-250 each), I would go for the K-3, especially now after using the K-5, K-5 IIs, and testing extensively the 55-300 (both smc and HD WR) against the DA* 60-250 on two K-3 bodies.
And if you can stretch it a bit, I'd go the K-3, sell your 55-300, and replace it with the HD 55-300 WR
-Heie