assuming that the only doubt about the legality of the catch is that it carried, then there is no difference in which offence is worse......
but it is such a complex issue that you can not blame players for either appealing or for not walking......except for those times of 'blatant' / excessive appeals etc.....bearing in mind that just because a player appeals / stands their ground does not mean that they think they have got it - they can be unsure of any number of things & on a close call it is better to wait for the umpire's decision.
umpires can be likened to the role of judges in a court of law - their function is to preside over points of law and the determination of 'fact', not necessarily if it is right / wrong (a function for the jury - commentators & spectators in sport). The umpires perform a similar role. If a player appeals / stands his ground he is in effect asking the umpire for a ruling - the umpire determines the 'fact' based upon the evidence, the outcome of which may not be right or wrong - but just read about it in the morning papers!!!!
Human error will always be a part of the game while humans are involved in any decision process. Players & spectators alike should have the grace to accept the good with the bad and get on with it. No individual (player or umpire) should become the target of any villification as the result of any such decision - except maybe for those instances where they failed to carryour their functions.
I think I have already mentioned sometime ago how 2 umpires 'missed' a spectacular diving outfield catch in a ODI because neither thought the player would get to it and they were both looking for the batsmen running 1 short!!!! Funny - I think the fielder on that occaision was none other than Martin Sneddon - involved in some more controversy recently!!!!
If the team is good enough a single decision should not effect the outcome in a Test - maybe for ODI's & that can be unfortunate, but should not affect the series. It's like the weather - stops you one series - saves you the next, but it evens out over time.