Wild, I'm a little confused by your question.
From what I can tell it sounds like you try for say a 3/4 ball cut but you wind up hitting it full?
Is that correct?
And the problem only appears (or is only apparent) when on the full sized table, not on smaller ones?
If both of those interpretations are correct I'd say the larger tables are making some sighting/alignment issues more apparent.
Put the cue ball on the brown spot and an object ball on the pink spot, hit the object ball full on and have it come off the top rail and hit the cue ball again. In order to do this, do you need the cue in the middle of the chin or to one side? If you have to move to one side or another in order to hit that shot you've likely got a dominant eye.
Extremely important: If you're not aligning/aiming a shot correctly, using side to compensate is a very bad idea. Eventually you won't know how to pot the ball without the side and you will run into trouble with position.
If you're not familiar with the concept of dominant eye, basically one eye is stronger than the other so you need to align the cue to the left or right in order to see straight as being straight. Dominant eye issues really aren't as noticable on small tables as the big ones which would explain why you don't have the issue or it's not apparent on smaller tables.
When you get down on the cue, is it square in the middle of your chin or do you have it to the left or right? There's nothing wrong with being to the left or right but it could be indicative of a dominant eye.
Personally a dominant eye causes me lots of grief because for me, how dominant an eye is seems to change depending on the shot. The reality is that it's unlikely to be changing very much, it's just that I'm so used to cueing in the middle that to deviate makes the shots look wrong. It also seems to change if I'm tired or partook in some weed but again that's likely just perception. On that note, IMO weed is terrible for your snooker game. I'm not anti-weed (I know some who wouldn't be able to slow down for 2 seconds if it wasn't for dope) but if you want to play seriously weed impacts too many areas of importance for it not to have a negative impact.
One of the best examples I can think of for a developing dominate eye and the associated issues is Hendry. In the past few years people have noted how Hendry's long potting is no longer what it was and IMO it's related to him having developed a dominant eye. Look at footage from the early 90's and you'll see Hendry has the cue going right down the middle of his chin. Then have a look at some recent footage and you'll see his cue is no longer in the middle of his chin.
Not sure if I've addressed your issue Wild but please let me know if I've interpreted your question correctly or you need clarification on something I've mentioned.