Hello Tao Parrot :-)
I suppose it depends entirely upon what the object is. Despite many opinions to the contrary, different meditational methods do provide different outcomes.
The focus on stopping thought processes itself (also commonly known as "samatha") is designed to stop the fluctuations of mental content so that a one-pointed focus can be obtained. I would be one who would suggest that this provides great therapeutic benefit, but little "spiritual" (although it is a necessary skill to develop before any other form of meditation will be effective).
The focus on observation of the contents of the mind (also commonly known as "vipassana") developed, essentially, as a Buddhist development on samatha techniques. This is also often referred to as "mindfulness".
Some schools of Chan/Zen take this one step further, and apply the hua-tou (similar to a koan) of "who sees these thoughts?" (or something similar) and use thoughts to provide a pointer to "him who thinks".
Being of this Chan tradition myself, not only would I disagree with the goal of "thought stopping", but would advise against it. The great master Hsu Yun said this resulting vacant void was a trap, akin to "soaking stones in water" and advised the practitioner to rouse him/herself against it and keep pursuing the question "who am I?" or "who is it who meditates?" or who is it who thinks?"
Fa Gong Shakya, OHY