This.
T-Mobile is the only HSPA+ network that is a worthy competitor to LTE, but even then, coverage of their ultra fast DC-HSPA+ is significantly smaller than Verizon's LTE network.
T-Mobile's HSPA+ will be faster then Verizon's LTE in some instances, due to the fact that HSPA+ can handle more users but has less coverage; whereas LTE can provide better coverage but decreases in effectiveness as more users access it. I read that somewhere, but forgot the source. Please correct me if I'm wrong.
As far as choosing the Nexus 4 vs the Note 2, there's no real comparison. If you want the Nexus 4, you want: pure Android and hate/dislike OEM skins, to root/rom/develop, fast updates over the shelf-life of the device, a device completely devoid of any sort of carrier interference, and a decently-spec'd phone at a cheap price (new).
If you want the Note 2, you are a power user that: doesn't value updates as much as Nexus users, wants the biggest screen you can get on a phone, needs the S-Pen and the functionality it provides, doesn't mind carrier bloatware (or intends to root and rom anyway) and doesn't care about pure Android.
Personally, if you're looking to buy the phone now, I would go with the Note 2. The Play Store is still out of stock, so if you're looking to buy a Nexus 4, you're looking at paying at least $500. The Nexus 4 is a great phone, but I couldn't recommend anyone paying over $500 for it, considering Google's price of $350.
Now, if the Play Store still had stock, I would recommend the Nexus 4 hands down. It represents the best value for the money right now. And if you can't afford the high price of the Note 2, then I will recommend shopping around for a deal on a Nexus 4.
Hope this helps, and good luck with whatever you chose OP.