So basically a 'normal' style Adventure Digivice (assuming the other ones you're talking about are the Blue/Orange ones aka Tai/Matts ones).
No, that's Airdramon who you fight at Jijimon's house when you have 45+ Prosperity points. Birdramon is this bastard:
(best image I could find on google), you face him when you go up the lift in the Great Canyon.
Greymon (who you fight when you have 15+ Prosperity Points) also destroyed me. if I had just a few more med recoveries/mp recoveries, I'd have won.
bastard.
Also on this note, I also have trouble catching Seadramon. Hoped I could do it with the old fishing rod but now I need to work on collecting cards to trade to Shogungekomon so I can get the Amazing Rod. (for those that have forgotten, Seadramon takes you to beetleland who has Kabuterimon/Kuwagamon that can upgrade your gym making it easier to get the stat points needed when you're training your Digimon to become an Ultimate)
Also in all my playthroughs, I've never recruited Nanimon (the one you need to see 5 times at different areas such as Ogre Fortress and Factorial Town)... I need to do that this time. Same with Ninjamon except I did recruit him to the city once. YEARS ago.