Back to jumping several versions at once.   
Everything has more options nowadays, including Snap, so it is imperative to find where the bakers have moved/grouped things. That seems to be the main difference between then and now; way more options/functionality and grouping of tools.

Hmm... Sounds like maybe you have your snap resolution set to very small increments maybe or you have the Smart Grid snapping enabled (which makes your snap res change as you zoom in or out... I find it annoying).
 
You should be able to snap like you are describing from S6. If you want it to land on the Measure lines right click the Resolution drop down in the Snap Module and select measures (or whatever you want). While you are in there check to see if Smart Grid is enabled. If it is it will have a checkmark beside it so click it to disable it.
 
Now Snap will follow only what you tell it to instead of changing all the time as you zoom.
 
Sorry if that's not your issue but it's worth mentioning. Smart Grid was a new feature in X2 I believe.
 
Cheers.

You might want to disable "snap to audio zero crossings" in preferences
 

NeckHumbucker
Say, I have an audio clip that I sliced somewhere between beats, and I want to copy it a few more times else where in the timeline. In Sonar 6, I'd press ctrl and click on the clip and move the mouse, and I can visually see while I am dragging, it snaps to same spot between the beats in every bar I am dragging over (given snap set to one measure).

Do you have "Move to" intesad of Move By" selected instead? Or maybe I don't quite understand what the problem is, snap works as expected for me.

Don't let the learning curve stop you from using Sonar. I started with CW with Pro Audio 8 and went through a lot of incarnations. Once you learn to use X3 you will be a very happy camper. Things get smooth and quick. And once you've let go of reaching for the familiar place things were in S6 and learned the new spots you won't look back with any fondness. X3 is so much more powerful than S6. Hang in there NeckhumBucker!

Beepster
Also I HIGHLY recommend Karl Rose's SWA video series on X2/X3. It goes on sale from time to time. Snag it and it'll show you where pretty much everything is.

Thanks for the recommendation Beepster.  For the OP - There are also some helpful freebies on my Youtube page. Link in my sig.

Sonar X3 Advanced Workshop: Virtual Instruments Revealed
Sonar X2 Advanced Workshop: Producer FX
 
Both seem to be dead links

Steve_Karl
Sonar X3 Advanced Workshop: Virtual Instruments Revealed
Sonar X2 Advanced Workshop: Producer FX
 
Both seem to be dead links

 
Hmm... thanks for that. Not sure what is going on there, I suspect it might be something to do with the new store setup.
 
I've changed it to a generic link for now.
 
Thanks again.

Thanks again for suggestions and encouragement to stay on course.
 
Michael: Timing anomalies in bounced was caused by stretched clips. I first bounced the individual stretched clips, then bounced the whole selection. First step of bouncing did the same timing anomalies, but second did produced the exact audio. I guess that's reasonable. Because I'd guess algorithms for real-time rendering and offline bouncing are different. Thanks for help.
 
Beepster: Turning off Smart Grid was one of the best things. Thanks.
 
Anderton: I haven't checked "move to/by". I will. Let me try to explain my problem more accurately.
 
I've done a couple of tests. But I still can't get the following behaviour work:
 
Here are the settings. Smart Grid off, Snap set to 1 Measure (not whole note, because time signature is 9/8, whole note isn't equal to one measure)
 
Say I have a sliced clip that starts at 10:01:240
 
In Sonar 6, if I copy it by ctrl+drag to next bar, it lands at 11:01:240
In X3, it lands at 11:01:000
 
In X3, I have to copy it and then nudge it, this works clip start on a nudgable grid like :240, but doesn't work if it start at something random like :233
 
or I have to stretch the beginning of the clip to 10:01:000, then copy it over.
 
If I have 10 clips in 10 tracks to be copied 20 times, it becomes tedious.
Thanks.
 
 

To do that switch to "Snap By". That will move the clip in increments of 1 measure so it should land right where you want. "Snap To" will snap it to the actual measure.
 
Cheers.

Yes, that's it! Thank you! I feel embarrassed now. Because I looked at those settings. I have to review each setting one by one and see their effect. 
 
I have one more question: How can I make Soft Synth Folder Template?
 
In a new project, I customized 8 audio and 8 midi tracks for a soft synth. I'd like to be able to save it, and insert it in other project when I need it.
 
Thanks again.