Here's a practical comparison of the field of view at different focal lengths (using a K-30 with Sigma 170-500mm lens). All shot from the same position (about 3-4m, say 10-12', from Oscar):
170mm:
250mm:
310mm (it was supposed to be 300):
400mm:
500mm:
As you can see there is a big difference in field of view (FOV) between 300mm (well, 310 in this example) and 400mm.
With long telephoto lenses, take particular note of the minimum focus distance (MFD) too. It tends to be longer on older lenses. The MFD on this 170-500 was 3m (about 10'), whereas on the Sigma 400mm f5.6 APO tele macro that I have now it is only 1.6m (a little over 5'), which is much more convenient.
You say that you want to use the lens for "nature and wildlife photography". You don't necessarily need a lens longer than 300mm for those purposes - it depends on how far away and how large your subject is likely to be. It also depends on how sharp the lens is. An image taken with a sharp 300mm lens (like the F/FA*300 f4.5 or DA*300 f4) and cropped might come out better than one taken with a mediocre longer lens. The greater pixel density of the K-3 (compared with the 16mp cameras like the K-30) is an advantage for cropping like this.
Even if you are considering the lens for photographing small-ish birds, don't rule out a really good 300mm lens such as those I mentioned. If you add a good teleconverter like the Pentax DA 1.4x WR to the DA*300 you will get a FOV the equiivalent of 420mm f5.6 (and with this TC, the details will be correctly reported to the camera). That can be a more versatile setup than say a 400mm f5.6 lens, and more lightweight and portable than a long zoom like the Sigma 150-500 or the Pentax DFA 150-450.
Last edited by Des; 01-26-2016 at 02:56 PM.