Hello Mark,
There are indeed many sequencers out there, some of which work across different operating systems and others don't. For whatever reason, I haven't to date got into a good habit of working with ordinary sequencers, so I don't have strong recommendations, but will mention a few. I've used many over the years.
Reaper: Full-featured but also lightweight. Reasonably cheap. Could well be a good option, especially as you can run it as an unrestricted trial version. I definitely recommend you try that.
For Mac, there is GarageBand which is free (apart from the premium you pay for a mac). Also Logic sadly went mac-only a few years ago.
Cubase is one of the main ones that you didn't mention. Kontakt is actually a sampler, not a sequencer, so it seems you were slightly mistaken in mentioning that.
FLStudio has very good midi editing facilities and also lifetime free upgrades. Struggled for years to shake it's 'toy' image, but it's pretty solid although perhaps not the best workflow for recording audio.
Sonar is another major one for Windows.
Ableton Live could be worth a look.
Tracktion: relatively obscure, different approach to UI design than others. I remember playing with the first version years ago and it seemed promising, might be worth a look.