The choice is yours: either way, it will be considered halal. The main thing is that it should die after coming in control.
Note: The relevant rules about catching a fish are reproduced below from the Masails of Ayat. Seestani, available on the web (see guidelines for URL):
Hunting of Fish and Locust
2624. If a fish with scales is caught alive from water, and it dies thereafter, it is Pak and it is halal to eat it, even if the scales are shed off later due to some reasons. And if it dies in the water, it is Pak, but it is haraam to eat it. However, it is lawful to eat it if it dies in the net of the fisherman. A fish which has no scales is haraam even if it is brought alive from water and dies out of water.
2625. If a fish falls out of water or a wave throws it out, or the water recedes and the fish remains on dry ground, if some one catches it with his hand or by some other means before it dies, it will be halal to eat it after it dies.
2626. It is not necessary that a person catching a fish should be a Muslim or should utter the name of Allah while catching it. It is, however, necessary that a Muslim should have seen or ascertained that the fish was brought alive from the water, or that it died in the net in water.
2627. * If a dead fish about which it is not known whether it was caught from water alive or dead, is bought of a Muslim, it is halal, but if it is bought of a non-Muslim it is haraam even if he claims that he has brought it alive from the water; except when a man feels satisfied that the fish was brought alive from the water or that it died in the net in the water.
2628. It is halal to eat a live fish but it is better to avoid eating it.
2629. If a fish is roasted alive, or is killed out of water before it died itself, it is halal to eat it, but it is better to avoid eating it.
2630. If a fish is cut into two parts out of water, and one part of it falls into water while it is alive, it is halal to eat the part which has remained out of water, and the recommended precaution is that one should refrain from eating it.