PROBLEM
CM11 (4.4.4) is undoubtedly a life saviour of S3... Works totally fine and amazingly fast... But on the other hand at the cost of few things only...
These are... Your WiFi direct won't work (mine is not working even I tried sharing pics on WiFi direct with S5 (lollipop updated) and with Google nexus 5 stock and Google nexus with CM updated).
Other thing is MOTO 360... Moto 360 won't get paired with CM11 on S3... Though it get paired on Bluetooth but when we open android wear app it shows a status of connecting....
I tried everything like rebooting watch... Rebooting phone ... Factory reset of watch... Everything and nothing happened....
On the other side when I tried connecting moto 360 with galaxy S5 (unrooted) it gets connected in no time....
Soy conclusion .. Though CM is life saviour of galaxy s3 i9300 but still with these limitations... Though I like CM a lot better then any other software indeed it is BT still I guess I have to change this in order to connect with moto 360...
On the contrary one having S3 must install CyanogenMod in order to actually use there phones at perfect speed of working conditions and without any lags.
SOLUTION
The only solution I left out with is changing my CM... So I installed one nightly version of CM11 and then checked its connectivity with moto 360 after installing android wear and updating all Google apps... And it REALLY WORKS... So this is the only solution go for change with CM and problem solved.... It get connected in no time.... And works flawlessly...