Can I please get specifics?
Okay so for the difference: Timid nature increases speed and decreases attack while Modest nature increases
sp. attack and decreases attack. As for the advantages its difficult to say since you have given no info on your team or its moveset. While both natures are popular, I prefer modest because it is a very good special tank. Trying to raise its speed even after an average speed stat isn't the best strategy but it is certainly not the worst either. Timid can really work well if it's good as a special tank by itself from its EVs and IVs. Timid can really work well in battles where your opponent's Pokemon's speed falls in the same bracket as yours which will give your Pokemon a chance to go first. However, its speed can fall short most of the time in competitive. The perfect role for Gardevoir has remained to be a special tank instead of special sweeper. Its main objective is to take hits from special sweepers as well as break special walls. The biggest thing with a modest Gardevoir is that you can easily give a choice scarf to boost its speed and then take out the opponent with its high sp. attack (same can be said for a Timid Gardevoir with choice specs which boosts Sp. Attack). So all in all you can really run a mixed Gardevoir with any type of sets as long as you have a good team, moveset and item to back it up. For a good moveset for each nature check the moveset question for Gardevoir on pokebaseQ&A.
Hope I helped! :)))