Having used Rekordbox DJ with both RX and RZ, I can attest that they both work very well - and have never encountered the problems you describe here.The sync function works well for those who use that, but require properly analyzed and beatgridded tracks to work. On some tracks, manual adjustments to the detected grid might be needed, but this is easily done in in the software. Are you familier with the Master Tempo feature? What are you syncing to?
Rekordbox can be quite demanding on your hardware, and depending on what OS you run, and which programs are running alongside Rekordbox, you could run into resource problems. My advice would be to check your drivers, update what can be updated, and make sure to close down apps and programs that doesn't need to run when you use Rekordbox. Also, as always, put your computer in Flight Mode.