transfer process(physics)

The one which is held upright would probably burn for a longer time.

When the flame is set up, it will heat up the surrounding air, the warm air will float while the cool air will sink. This set up a convection current. Heat is then transferred by convection.

When the match is burnt, the heat will be transferred to the unburnt part of the match by conduction and convection.

If now the match is istilted, then the heat transfer by convection will be poorer than that held upright. Hence, it will take longer time to transfer heat if the match is istilted. As a result, it will take longer time to burn the unburnt part of the match if it is istilted.