I am using stock rom (gingerbread) at the moment and experience none of the lag you refer to. I also tried some of the ics roms and also no lag.
The only time my phone 'hesitates' is sometimes when I unlock it as it switches from widget locker to lock screen. Now as it is a 3rd party app doing it, I can hardly blame the note. I love my note and even got rid of my galaxy nexus and asus tf101 when i got the note.
Sent from my GT-N7000 using xda premium
Don't be shy to hit that 'Thanks' button
Samsung Galaxy Note 3 - Stock 4.4.2
Samsung ATIV Tablet GT-P8510 - Windows RT 8.1
Retired / Sold -
Nexus 5 | Nexus 4 | Nokia Lumia 925 | Samsung Galaxy S3 | HTC Desire | HTC Desire HD | Samsung Galaxy S2 | Samsung Galaxy Nexus
Samsung Galaxy Note 10.1 (2014 Edition) | Nexus 7 (2013) | Nexus 7 (2012) | Samsung Galaxy Note | Samsung Galaxy Tab | Archos 80 G9 | Asus Transformer | Samsung Galaxy Note 10.1 GT-N8000