I have owned a number of Klipsch speakers - KLF-30, CF-3, Heresy, and currently Quartets, which are like the little brother to the Fortes.
I went down the Thiel rabbit hole recently. I bought a pair of CS 2.3 speakers from a friend at a great price. I liked almost everything they did, but for me they were too detailed and had a brightness to them that I just couldn't get past. I heard great things about the 3.6 and found a pair of those at a reasonable price. They had more presence and body and the imaging and soundstage were great, but the sound signature was almost identical to the 2.3. I bought some high powered solid state amps to see if that would tame them, but they didn't. The brightness wasn't there on everything I listened to, it was recording dependent, which is not necessarily a flaw of the speakers, just them revealing whatever is there in the recording.
I believe that I'm more sensitive to brightness than most. I know many people love the Thiel sound.
One of the knocks on Klipsch speakers is that they can also be bright. They can sound great with a warmish tube amp and are only going to be bright if you like to listen at rock concert volumes. People tend to think of Klipsch as "rock speakers" because they can play really loud effortlessly, but where they really shine is with jazz, vocals, acoustic stringed instruments and the like. I don't really agree most of the time when people say that a certain speaker is best with a certain type of music, but in the case of the Klipsch I think they do better with some types of music than others. They are also very revealing, but are not going to be the imaging / soundstage champs that the Thiels are.
If you like the sound of the KEFs, I would consider getting some better ones. You might be able to find a pair of Ref 1s at or near your budget. You might eventually need to upgrade your amp and add a sub or two, but if you want imaging and clarity, they are hard to beat in that price range.