Thank you everyone for your replies, they are much appreciated and make me think that this is more a technique and/or perception problem and that the gear is just fine.
Here are 3 shots that best illustrate my issue. Despite the sharpness being good at first glance, a 100% zoom reveals that a lot of the edges are soft and hat the colours seem to "spill" on one another. I have never encountered that before and this is why I find it surprising.
Now, I've noticed a couple very interesting things that I hadn't noticed before and seem to be at the root of my problem:
1. After trying to take the exact same low-light-ish picture with my K3 and t5i, at equal ISO and aperture, the t5i comes up with a faster shutter speed than the K3, so it seems that the K3 needs more light (because of the higher sensor resolution?) and therefore more precautions in low-light conditions.
2. All the pictures that seem to cause trouble are taken in non-optimal lighting, and have some sort of fine, repetitive detail (tree branches, ...). Looking at pictures from the 2nd link Dsims posted reveals a similar look to them. This makes me think this is just how the lens reproduces this sort of details.
I think the solution may be first to seek better lighting or stabilization, and work with DoF better. Let me know what you think
Thanks for your help and please forgive my inexperience!