I have used MIDI files from Sonar and Pro Audio with Logic and Cubase. Though I have Reaper I have never done much with it. (I own a license) But I suspect that it could be any one of a number of things. First is the tempo the same? Then as mentioned is the sample rate the same? Also Sonar can adjust its tick resolution I don't know what that is with Reaper or if it can be adjusted. That is something I would look at. Plus look at the MIDI in Reaper's PRV and see if it looks right.
Now as I started I have used MIDI files between those named DAWs and have never had a problem in one or the other sounding any different from Sonar or for that matter Pro Audio.
BTW as an aside, of all the DAWs that were mentioned above only Sonar can load a MIDI file as a native file format. One does not have to import it in Sonar. This alone can have interesting results if it is imported into a project with its parameters way off.
The short answer, to my knowledge it isn't a Sonar problem. Cakewalk the grandfather to Sonar was a MIDI sequencer.