Hi,
I could be wrong, but I get the feeling that you are comparing the clock frequency of the CPU of your phone with the radio frequency of your WIFI router. The two are completely different and will have no interaction whatsoever.
Now, there will be a difference between the 2.3GHz and 5GHz bands of your router. The 5GHz band will likely carry data at a higher speed. However, while this is mostly always true, it is not a given fact. It all depends on which other devices are in your house (DECT telephones and Bluetooth devices share the same frequency bands to name but two examples), how your house is constructed (how many walls lie between you and the router and how thick they are or how much cabling/pipe work is present) and what sort of reflections and other interference you suffer from. Also, what your neighbours are doing will be critical (i.e. how many other WIFI signals are around). You could try to change the channel that your router uses and see if you get better performance.
After rereading your question, you could also be asking about the laggyness of the user interface, so feel free to clarify if this is the case.
Regards,
Eric.