The issue is, to what extent one can incorporate another's mark within his own and still not be liable for trademark infringement.
The basic tenet of trademark law is to avoid any confusion in the market. And therefore, even a slight likelihood of such confusion gives rise to a cause of action for trademark infringement. For example, "PerfumeBay™" was held similar to "eBay®" because the former completely incorporated the latter, which was off course a strong mark in itself.
Similarly, any likelihood that one mark would suggest an association with another brand, would also be construed by a similar standard. For example, if a third party sought to register LIFE IS SHORT, Caribou Coffee might argue that it suggests an association with it's registered slogan LIFE IS SHORT. STAY AWAKE FOR IT®.
In addition, the more distinct the registered mark, the more likelihood that it would cause confusion in the market. For example, using Haagen-Dazs® in the slogan would more likely give rise to an action for infringement, rather than using some descriptive mark, may not.
Thus, any comparison in your question would depend on the foregoing factors.