All the posts here seem to say one of two things; first player is overpowered; Replay wonders are overpowered.
The truth in my experience is, neither of these statements are true
Starting a game, do I want to be player one? Yes of course. If I don't get it, is that game over? Not at all. I generally get the advantage in age two when the resources are stronger and I can start to control things
Do I want more replay wonders then my opponent... same question... Same answer
The only games I felt were more like swimming upstream was when you got the perfect storm of both these things.
Player one gets one replay wonders in the first draft, then three come out on the second. Therefore leaving a 3-1 advantage to player one in this area
This then means player one not only gets more goes, they can flip the order at the end of age one and still have first pick in age two or save these wonders to control the board on the later ages. (A replay in age three is very powerful to get first choice of cards at the end of the age)
If you really wanted to change this aspect of the game and 'balance it' you just need to prevent this scenario.
I think Chris Me came close to what I would suggest as a solution with a slight tweak
With the way bga does the drafting in two sets you could simply give player two the choice of whether they wanted first pick on the first set of cards, or if they wanted to wait and get first pick of the second set (don't give player one this choice as Chris suggested as gives them even more power than current)
This is a common pattern in a lot of standard deck card games where you can take or pass to your opponent
If the first set of four wonders had one replay, as player two I'd likely take. The worst you should ever really get is player one having 2-1 replay wonders if you gambled wrong. 3-1 should never feature
This I believe would work well as a house rule. The key being not to let player two see both sets of wonders before deciding if they want first or second pick so they have to make this decision. The revealing of the second set of wonders then kind of mirrors the whole card turning and reveal process in the game
As with many other suggestions, it's very unlikely ever to change here but thats my thoughts