To start - I've just bought a M1200R following a couple of years on a 2014 Tuono. I have to disagree with your observation: The Tuono has more feel and more weight over the front wheel, the Tuono is a very well sorted handling bike, taking a lot from the RSV4. The Monster is good, I just bought one, but is more relaxed in its riding and handling and isn't as sharp as the Tuono or a BMW S1000R in my hands. The SDR, I could see where you're coming from with that as the KTM is more motard in its riding position.
I would agree re. the Tuono. However, it's not nearly as pretty as the Monster, it's not really naked, and has fewer trick parts. Tuono aside, the Monster has consistently beaten the S1000R and KTM 1290 in magazine track tests, despite a 10-20bhp peak power deficit! In the 'Rutter test' (PB), it's the quickest naked bike ever tested around Mallory park with the exception of the Tuono, and it beat the 899. I've switched from a 2015 R1 to the Monster, and for me, it feels very nearly as agile and sharp, and inspires a similar level of confidence in corners. Adjusting the suspension settings to the 'Sport' (see handbook) improves composure and agility, at the expense of a slightly firmer ride. A free breathing exhaust makes it 'feel' more focused too.