Re: Router.
Have you tried downloading the Apps on 4G? (assuming you have a data allowance) and comparing the results with your network connection?
The posted link above can be used for both types of connection, wired and 4G via the appropriate browser. Compare the results of the network speed with that which is promised, for instance, if you are paying for 30mb (say), does the network speed come anywhere near that?
If the 4G connection is faster, I would suspect the router if you aren't getting anywhere near the promised speed on your network or as Realspeed said, the distance of your phone line to the web server could be a factor. It wouldn't hurt to get the line checked.