Which cordless phone is better a 2.4 ghz or 5.8 ghz?

Question

does one have a greater receiving distance from the base than the other

Answer 1

neither!!

I would go with the Panasonic DECT 6.0...!

These channels are reserved exclusively for voice communication applications and therefore are less likely to experience interference from other wireless devices such as baby monitors and wireless networks. DECT devices made for use in the U.S. use the brand DECT 6.0 to distinguish them from both DECT devices used elsewhere and U.S. cordless equipment operating in the 900 MHz, 2.4 GHz and 5.8 GHz ISM bands. The "6.0" is a version number (as in software), not a spectrum band; the term "6.0 GHz" for DECT 6.0 phones is incorrect, since it operates at 1.9 GHz.

Answer 2

The higher the frequency, the less likely the signal will diffract around corners.  

The 5.8 GHz will not provide a better distance or range for general use; in fact it is poorer for this.

The 2.4 GHz can suffer from interference from wireless routers, microwave ovens, other 2.4 GHz phones, etc.  If this is the case you may find a 5.8 GHz is better.

Many typical users do not see a difference.

It really depends upon your needs and circumstances.