It is an interesting question. First-class cricket has the same general format as test cricket (no limitation on overs, so the emphasis on bowlers is to get batsmen out rather than simply restrict runs, and the emphasis on batters is to bat for long periods). On the other hand, we can all think of players who have been successful playing for their province, state or county, who were unable to make the step up to international level. So performance in first-class cricket is perhaps the better measure of a player's skill set while performance in ODI's the better measure of his temperament, and also of whether there are technical flaws in a player's game that will be found out at the highest level.
I don't know what the correct answer to this is. My guess would be that the stronger is the competition at sub-national level, the better would be first-class cricket as a predictor. So, for instance, I would expect that first-class cricket is a better predictor of Australian players' success at test level than it is for New Zealand players. And I suspect that, overall, even in country's with weak domestic competitions, first-class cricket would be the better correlate, but it is just a guess.
But this rasies a different question: What measure of performance in ODI cricket would be the best measure of success to use in a correlation with test averages? This rises again because of the different format. Batting and bowling averages are a very good measure of performance in test or first-class cricket. Yes, we need to adjust for the conditions in which different players have played, and the quality of the opposition, but in general maximising your batting average and minimising your bowling average is the way to maximise the chance of your team winning. In ODI cricket, this is not the case. The relative importance of runs and wickets changes depending on the game context, so that averages are not a good measure of a player's contribution to his team. Naturally, I would prefer a measure like the player's contribution to the WASP, as maximising that is what a player should be doing to help his team win.* But let's say you had two players, one with a better average and one with a better WASP-based performance. Does the difference arise because the latter is a better player in general, or does it indicate that the former has a skill set more suited to test cricket. I really don't know. Maybe that is a future Honours project.
* Actually, WASP-based measures would only be useful for comparing players at a similar point in the batting order. My student, Marcus Downs, has been writing an Honours dissertation this year developing an adjusted WASP-based measure that enables better comparisons across players with different positions in the order, but this is secondary to the main point.