I assume you're talking about FileMaker WebDirect?
There are numerous topics already floating around this forum about why just converting from FM12 to FM13 WebDirect can cause slow performance. Try searching for WebDirect Performance and you should find plenty of reading material.
A viable switch from FM12 (hosted or IWP) to FM13 WebDirect should have a gameplan for developing or adapting your solution for WebDirect, straight conversions without these considerations are not recommended.
Here's a great video about optimizing solutions for WebDirect:
There are probably problems with your existing FM12 solution that are causing the performance issues in WebDirect. WebDirect is not a replacement for the desktop version of FileMaker. It is a new platform that has serious considerations for deployment.
Mike has it right. If you just take your typical FileMaker database and switch on WebDirect... it won't necessarily be very snappy unless you do some clean up to the layout. Even then, WebDirect is not a replacement for Pro. Use WebDirect to Augment your existing deployments. This topic is covered in the Youtube video listed above.
Another factor which can be huge is how you are connecting to the URL via the browser. The odds are good that your internet connection is via a WAN network and your FMP connection is ethernet or other LAN setups in the office.
The performance difference between WAN and LAN connections is huge, and that's before the limitations of WebDirect.