The International will work on HSPA+21 speed, which I believe is AT&T and StraightTalk. It will only work on T-Mobile's HSPA network if your area has been refarmed to the 1900MHz frequency. Check airportal.de to see if it's in your area.
The T-Mobile version will work on both, T-Mobile's HSPA+42 network, and AT&T's HSPA+21 network. And it will automatically work on T-Mobile's LTE network once they complete it. The International one has no (and will never have) LTE. The only issue with the T-Mobile Note 2 is that is doesn't have the Multi-Window function and there's no telling if/when it will come and it will take longer to get official updates.