I don't know what game you're talking about, but I'm assuming you mean Generation V, so I'm going to go over Black and White and their sequels. Generally it's very hard to get a Larvesta to evolve into a Volcarona, especially if you're using it before the postgame. In Black/White it's only obtainable if you're given a Larvetsa egg from a Pokemon Ranger on Route 18, and it evolves at level 59. If you have the patience, it certainly is worth evolving it into a Volcarona, though. In Black/White 2, it's MUCH easier to get a Volcarona, as there's a level 35 one in the Relic Castle. Volcarona can learn Fly, which is very useful in the field, but this isn't a very good move at all as its Attack stat isn't good.
Alright, so Chandelure is all around easier to obtain (Lampent evolves at level 41, so you don't have to do as much levelling up) also having a higher Special Attack than Volcarona. I'd personally go with Chandelure if you're playing Black, as getting a level 1 Larvesta to 59 will take a very long time. For B2/W2 Volcarona is easier to get and probably the better option. It has better Speed than Chandelure, and one thing that I haven't mentioned is that Chandelure, being a Pokemon that evolves using a stone, can't learn many moves at all by levelling up, so you'd need to raise a Lampent to a very high level in order to get the best moves for it. But with Volcarona, it learns Fiery Dance at Level 1, meaning you just need to go to the move relearner to get a fantastic move that also boosts your highest stat half of the time.
For competitive there isn't really an objective answer either. That being said, of course there are situations where Volcarona would be a better choice than Chandelure and vice versa. They both have their pros and cons, and you need to adjust your team accordingly to which one you use. Volcarona unfortunately has a 4x Rock weakness, making it lose half of its health to Stealth Rock. You need to run a Pokemon with Rapid Spin or Defog in order to effectively run Volcarona. Chandelure also has a Stealth Rock weakness, but it isn't as prevalent as Volcarona's.
They both can perform their different sets effectively, it just depends on what generation and tier you're playing. Volcarona is more of a sweeper while Chandelure is more of a wallbreaker. You can use whatever sets you want as well, e.g. running a scarf on Chandelure because of its average speed. Anything can work if you set it up correctly, so keep that in mind. It depends on what role you want filled on your team.