well, both can be right. the coding does have significance, but i'd go with hosting company if it's veeery slow. I'd recommend taking a new one. godaddy.com used to be good, but then i had issues with speed also, so i switched to host1plus.com now. no problems yet for two years now.
Have your devs profile the code! Set up xDebug and run it, it will save a profile that you can then open and see where the bottlenecks may be in the code. If you don't see any bottlenecks in the code, you have a file that proves it isn't the code.