EA vs Minbari can be very good... if the EA knows he is facing Minbari then he can take scouts, long-range fighters, high AD ships and split fire, prioritize weak(er) targets such as Tigara, get up close and into the correct arcs. It's a lot harder in tournament/blind fleet play of course but there are many ways to beat Minbari which are not obvious to the new player. Each of these tactics gives you only a slight improvement in your odds, but combining all of them gives you a good chance. A stealth 5+ enemy can often be brought down to 2+. In fact I would say EA/Minbari is one of the best match-ups along with Narn/Centauri.
Drazi are a bit of a one-trick pony, yeah. You could try Claweagles to mix it up a bit, they aren't that great a ship but they're a fantastic distraction because they scare the hell out of people. Drazi don't ever take anything above Raid, and mostly stick to Skirmish. Strikehawk and Warbird are your best ships, especially in squadrons (although you do need init sinks too). Don't forget you can do Attack Run and Track That Target - although both have high CQ checks so only use them if you have to. Just remember if someone puts Shadows on the table, run away fast... unless they take a Shadow Ship, of course, in which case, charrrrrrge!!!