There is a bit of a history with CiviDiscount. I did a whole lot of work on it against 4.4 & did a PR for a version with quite a lot of changes. It was partly merged & then they forked for 4.5 & the rest was merged. The upshot being that I don't know too much about the state of the 2.5 branch against 4.4 but I continued with my work on 4.4 & the version we have been using against 4.4 is being called 2.5.1 - although it's not the official branchhttps://github.com/eileenmcnaughton/org.civicrm.module.cividiscount
Both 2.5.1 (4.4) & 2.6 (4.5) include schema changes to the cividiscount tables, so it might be worth trying 2.5.1 but definitely try on a test site first.
Note that 2.5.1 / 2.6 make it possible to determine your own criteria - so we have a site where specific line items are discounted for all students, as defined by a custom field
I would also note we had to patch core a bit & those patches are likely to be in the 4.4 LTS release - I can't recall whether it was core patches of the cividiscount version that got it all working but we definitely have fine-grained discounts working - ie. discount particular membership types within a price set for people over 80 years old (I think we have another bit of custom code that removed ineligible membership types from the price set )