What is the best way to raise handle bars I have bought a second hand 19 inch frame and I am normally used to a 20.5 inch.

The bike rides OK but I would benefit from raising the handlebars.

I have read about fork steerer tube extenders and adjustable bicycle stems.

I personally think the fork extender would be a better way, are there any advantages or disadvantages to either?
A stem with a greater angle and rise, potentially coupled with a riser handlebar will be a stronger solution than a steerer extender. If you are doing casual riding on flat ground a steerer extender is probably OK. If you are riding rough terrain and putting a lot of force through the bars an extender may not be able to handle it.