The DNS for either ISP may differ, the ISP could block an offensive or competitors web site.
Your skill at the use of NSLOOKUP or TRACEROUTER is required. I only note the names of the tools which you teach yourself about with google.com.
I have two different IPS's. My browser(IE6) will connect to one IPS and not connect to the other one. I can sign in and connect to both of the providers. What would keep the browser from locating the entered address in one and not the other?