Using two different tools should be ok, provided they are both good tools. One of my climbing partners still climbs with one hummingbird and one old school chouinard. It's fun to watch him clear bulges. He's upgrading to the new curved modern stuff after 20 years. I don't know if there would be any advantages to having two different tools. It isn't as sexy, and we all know how image conscious ice climbers are, especialy here in new england.
Trad- I took my adze off after I realized that I NEVER used it. You'd be suprised what you can do with a hammer. I was too cheap to buy another hammer, so I just left the back of the tool empty like the trango ones. Works great, swings even better. I think its worth trying out.