PDF/X-4 importing to Illustrator

Hello,

After reading about pdf options on Adobe help I have discovered that using pdf/x-4 standard produces a good pdf from InDesign. I need to be able to print good quality on a big laser printer.  I chose 'press quality' and then chose the pdf/x-4 standard.) Prior to this discovery I was always opting for high print quality and NOT choosing any standard.

This led to a quality difference as seen in the following image files. 

1. Pdf made using pdf/x-4 standard. (The green background with text is a .psd file imported into the original InDesign file)

2. The same InDesign file but the pdf was made using high quality print option and NO pdf Standard chosen. Notice the loss of definition of the text and duller / darker colour.

My question is this.....

If I import the pdf made using the pdf/x-4 standard into Illustrator then the whole image seems to revert back and the text on the green background becomes fainter again i.e. as if I had produced without choosing the pdf/x-4 standard.

Is it possible to correct this??  What am I doing wrong ?

Many thanks in advance if anyone can help!