Is it acceptable to compare your experimental results with the claimed results from another paper?
In theory, if a result is published you can use it as is. 

In practice, it is better to replicate it yourself. That way you can really make certain you are comparing like with like. Research often involves a very long chain of decisions that cannot all be published in an article. Good research documents that somewhere else, but it is easy for honest mistakes or omissions to seep in. So that way it could easily happen that Mr. X's design is subtly different from the design used in paper P, and the difference in result are due to that difference in design rather than the difference in method. You can rule that out by replicating the results in paper P yourself.