On the Avantasia song, he does sound better. But there are a few reasons for that, and not all of them are things Geoff gets to take credit for. Some of it is, as I said, that he does actually do a better job on Seduction of Decay than he has on his own material dating back quite far. Kudos to Geoff for stepping up and delivering a good performance. I suspect, although I have no proof, that a big part of Geoff delivering a good performance is Tobi pushing for a good performance and not settling for anything less. I say that because Avantasia is totally Tobi's baby and he isn't going to let a song suck because a vocalist phoned it in. He is a control freak, and he has high standards. I suspect he was much more hands-on in coaching Geoff than what Geoff gets when working on his own material. And given that this is clearly a Tobi project, I don't think Geoff would have had an issue with that. He's smart enough to know he can't come into someone else's house and call the shots like he does with his own stuff.
Part of it that has nothing to do with Geoff is that Tobi props him up. There is a LOT of Tobi harmony that is filling in the holes. It doesn't jump out as not being Geoff because Tobi knows how to blend with Tate rather than steal Tate's thunder and take the lead himself. If you listen carefully, there are lots of spots where Tobi is doing that (and plenty where you really can't tell whether the lead is Geoff or Tobi).
There is also a lot done in production to make it sound good. It is hard to tell how much of it is effects, how much is layering a lot of vocal parts, or what have you. But it isn't just a one-take lazily slapped over the instrumental track, which is what a lot of Geoff's parts in recent years have sounded like.
Honestly, Tate should take a cue from this experience and use it going forward. If his studio performances were passable, I might be more inclined to give him a pass in a live setting. I mean, a lot of his live singing habits, his abuse of his voice, and his failure to warm up and do other things to get his voice in shape are his own fault. But still, live vocals are difficult, and I find it hard to hold someone Geoff's age to the same standards I would hold him to when he was younger. But there is no excuse for not putting out a solid studio performance on his albums. There are lots of things singers do to make their studio recordings sound better, and most of these are no-brainers. Take it line by line. Rest in between. Re-do until it sounds right. Use lots of layers. Let yourself be directed by someone with a good ear, and listen when they say something doesn't sound good. Use proper effects when necessary. Let the vocals be worked on in post-production. Get some solid harmonies from other good singers. It doesn't matter that it can't be replicated live. If nobody likes the studio versions of the stuff you are putting out there, they probably aren't going to come see you sound even worse in a live setting.