I'm more familiar with the DECODE version of Birdy which I thought was a fun time though I don't know how it compares to the original OVA version.
Decode is objectively better, but it's kind of it's own thing and has nothing to do with the then on-going Manga. Ex. None of the Villains, including Birdy's love interest, Nataru, are in the Manga.
The OVA has amazing animation and a promising story that leaves you wanting more, but is confined to the 4 episode restriction; it's also hard to compete with
Decode's OST due to having been done by the Jojo guy.
I have a lot of personal nostalgia for the series. I initially discovered the OVA during Middle School when pretty much every Anime was uploaded free on YT. I was so bummed when I finished it as I wanted more, but then immediately found out that Decode had just started to be released. Every weekend that Summer, I remember sneaking past my parents bedroom at 2am to turn on the computer and watch the latest episode with Fan Subs. lol
The Manga is a good read and is still being fan-translated (28/33 Volumes complete). It might catch a lot of people off-guard though, especially if you've only watched Decode, as it has a lot of dialogue and focuses detective work, political/racial discrimination talk, and references to Japan's war crimes during WW2. The first Volume or two also doesn't have the best translation and tends to mix up the identity of the Gender-Fluid Main Villain. It's very much a Seinen Manga.
Unless Discotek works up another miracle, due to licensing issues, it's doubtful we'll see either Anime get re-released, but both are avaliable to watch for free in-full on YT.
