Practice on the big table...yes, it's tougher to navigate the patterns on a bar box, but the improvement on your shot making and CB control on the big table will pay you huge dividends when you move down to the bar box. Well worth the effort. It's easier to adjust to the tighter confines of a bar box after playing on 9 footers all the time than moving up to a 9 footer after only playing on bar boxes. A shot that will go on a 9 footer will always go on a bar box, but you'll find that shots you make all the time on a bar box will rattle on you on the big table.
Obviously it is best to practice for a tournament or match on the equipment you will be playing on. Aside from that though, generally speaking big table practice can have benefits when going to the bar box - as you mentioned long shots don't seem as long etc. Don't see much benefit to practicing on a bar box to improve your big track play though.
I have an 8 foot at home but play league mainly on barboxes. I can tell you if I warm up on my table then go to league I'm at least a ball better. Tighter pockets at home leads to better stroke and the long shots on a barbox look like nothing. Just my .02 cents.
Most of my practice is done on a 9 footer with shimmed pockets while most of my league play is done on a bar box. During practice I try to focus mostly on my shot making and a few other things. The thing I try to stay away from is really playing a game on the big table. I have found that in the past when I do this my speed is so incredibly terrible that I am constantly out of line when I go to the bar box.
It depends. I think there is an element of confidence that can be gained from playing on "easier" equipment that translates really well to other conditions.
Before league, which is on bar boxes, I always warm up on a Diamond 9 footer. I get to a point where I'm confidently getting out on that table, then come down to the bar table and break and run like nobody's business. I think it's a huge benefit to warm up on a bigger table when possible. Yes there are ball speed issues in how you move, but I think that's a minor adjustment compared to the shot-making benefit you get.
I agree it's good to practice on a big table. But at home I have a 8.5 foot table for two reasons: I have to use a bridge too much on a 9 foot, which is annoying. And 8.5 is the biggest that would fit.
Don't let anyone tell you differently....the bigger the table and smaller the pockets, the better player you become.......a 5x10 table with 4 5/8" pockets is ideal.
You will play better on a smaller table versus a larger table but that doesn't mean that moving the ball around won't land you in trouble or a dumb scratch on the CB.