It depends a bit on your situation.
You want shields when:
- It's earlier in the game, and you can get enough shields that most enemies can't crack them.
- You have a limited crew, and might have to abandon pilot or engineer.
- You have drone systems and a defensive drone you can afford (energy and drone parts).
- You have mostly nickel-and-dime weapons (burst laser, anti ship drone, ion cannons).
You want engines when:
- You have a Zoltan shield.
- You have a serious vulnerability (mantis or crystal b, rock a) and might have to run.
- You have a location quest you're eager to get.
- You have an item you need to buy.
- You rely on an all-or-nothing weapon (beams, bombs).
Unless you're dramatically in some of these camps, you want one or the other. Starting engi b should really start with shields. Starting zoltan should really push engines.
The reason shields are better if you do consistent, gradual damage is that, if you damage the enemies weapons and the enemy gets a chance to repair them, the enemies weapons go out of sync, and the computer won't wait to sync them up again. Once that happens, a ship with good shields is far better off than a ship with good evasion.
Unless you have zoltan shields, neglecting shields means taking more risks, but a ship with five engines and good cloak can almost always escape before taking damage. That means you can escape, which means you can afford to hit a store or a quest or both, even if it means you'll have to hit the rebel blockade to get to the exit.