Do not go. I've been to Kanchanaburi (mainly known for the bridge over the River Kwai) and the advertising for these is prevalent, but I didn't go myself (for the above reasons). I know a few people who have gone and they report it's not a pleasant experience. You get a photo opp with a drugged tiger and then hurried out for the next person. Certainly nothing to base holiday on.
If you want to go a see big cats, see them in the wild. Go and do a safari in Africa (I've done two, wildly different but both totally amazing, and was lucky enough both times to see a lot of lions). You don't get to touch them, but if you're lucky, a big ass wild (wide awake) lion will sit on the bonnet of your jeep for a bit - because he wants to and who the hell is going to say no!!
Seeing wild tigers is much harder, I did a mini safari in India but didn't manage to spot one - shame
The thrill you'll get from spotting a wild big cat is much greater than you'll get from 20 seconds standing above a doped tiger in a poxy zoo.