I would think 18-135mm is a better choice for you since you have a budget concern.
I personally am using the 18-200mm. I went through many of my shots, 18-135mm covers 90+% of the focal length of my shots. I hardly need to shoot in the 135- 200mm range, other than in some rare occassions of course.
Unless you shoot more at the long end, otherwise it is not justificable in your case to pay S$1k more to make up the 135mm-200mm, that you might hardly use. And if you shoot more at the long end, then adding a 80-200mm later would be a much better choice. Comparatively, 80-200mm with F2.8 would give you much sharper image, and make up the VR that you need to step up to F5.6 all the way to 200mm on the 18-200mm.
So in my very personal opinion, 18-135 mm should be your choice considering your buying criteria.
After owning a DSLR for a while, if given a chance to buy a new cam set, likely config would be 17-50mm, 70-200mm VR, 50mm. I wont go for a MPV like the 18-200mm any more. Dont get me wrong, it is still a good lens especially the convenience of using just one lens; but just that there are better combinations.
I am now waiting for the 17-50mm Tamron. I will still keep my 18-200mm, but not sure if I will still use it once I have the Tamron.
Hope my input helps.