Thanks for your question!
It's hard to know what might change for your hop count if you changed ISPs since you and your friend are geographically in different locations (even though they're only 10 km away). That said, the number of hops doesn't necessarily mean anything about the latency or packet loss of your connection.
To compare your connection with your friend's I'd recommend that both you both use PingPlotter to monitor the IP address of the game server for the same 48 hr period. During that time, make sure to play the game that uses that game server and note the times when you're playing the game and what your experience was (lagging, rubber-banding, etc) if you're having issues. After 48 hrs have your friend send you a pp2 of their trace (File -> Export Sample Set (pp2)) and import it into PingPlotter (File -> Import Data) and pull up their trace and your trace side by side and compare your latency and packet loss results.
This would let you know if it might be worth it to switch ISPs.
Let us know if there is anything else we can help you with!