Call dropping is due to lack of signal. HD calling improves the audio fidelity of the call. Two totally separate issues.
Something tells me that you chose both carriers based on something other than actual measured coverage (using a phone on that carrier in the place you need coverage). No phone will give you good voice quality in a bad signal area - Verizon will sound like the caller is under water, T-Mobile will sound like the caller is way too autotuned (like Cher). It's called "going digital" and it's like static on an analog signal.
Find the carriers that have solid coverage where you need coverage (talk to someone on a friend's phone and, if the signal is solid as you move around, you have good coverage for that carrier for that location. And by location I mean square feet, not neighborhoods. It doesn't do you any good if Verizon has terrific coverage in your building, but your office is in a dead spot.) Once you find a carrier that has solid coverage every place you need coverage (and you may not, depending on where you are - then you choose the least bad carrier), use that carrier, and choose from the middle to top of their phones. (The "99 cents with a 2 year plan" phone will usually have a bad signal in good coverage areas.)