You'll find a good end-user HE-34/HR-44 comparison here:
My short answer is "Way different and worth it," but I need to add both are OLD MODELS. If you're upgrading, you might as well insist on an HR-54.
You need to know #1: If you're out-of-contract, you should require new-in-box (not refurbished) and newest-model equipment at no additional cost to you (other than a new 24-month contract). Getting you back into contract is a high priority for AT&T, so you have good leverage to get precisely what you want.
You need to know #2: all model number "HR-xx" represent the same model. The only difference is who made it, represented by the appendage "-x00." This rarely makes any difference in performance.