Perception is for observation, Investigation is for deduction.
Some of this answer will be observations on how Wizards has done it so far and some of this will be logic, and some of it will be mechanics.
First for the headline question. It depends. when to use Investigation, and when to use Perception is not entirely clear yet, and I'm hoping we'll get more guidance in the DMG late this year. The guidance from the rules is that the two skills mostly seem to differ in the methods by which they are found.
Depending on the exercise, either, or both of the skills may be used.
For passive checks, you're almost always looking at Perception being the skill of record. While all skills can be used passively, some skills make more sense than others. Perception is the hallmark passive skill, whereas investigation makes less sense as a passive skill.
If the character is alert to the possibility of hidden objects/traps, but not actively searching, he's using passive perception.
The guidance for this seems to be (though we can't confirm yet), that the DC for actively looking for something is regularly about 5 less than the DC for passively looking for something (or sometimes actively looking always reveals it).
So here's how I would play it. Traps can be noticed with perception passively (usually DC 15). If the PC is looking, ask them how they are looking. If it's observational, then use Perception. If it's deductive, use Investigation. When they are searching for items, again, either skill is appropriate. This is somewhat counter to how WOTC has written adventures so far. They are always written to use perception to notice traps. Passive with a higher DC and active with a lower.
Investigation also has broader uses such as when you are trying to track clues, or put something together. It's also a great "roll for a hint" kind of skill if your PCs get stuck and need some help figuring out what to do next.
You cannot do better than follow the advice in the Angry GM article. In summary: have only one or two types of traps that are detectable by the players.
What the article does not address is using traps as battlefield obstacles which is the way armies use "traps" like landmines and barbed wire. These things do not stop enemy armies but they can channel movement - clearing minefields and barbed wire takes time. Either the enemy takes the time and you can redeploy to meet them as they come out of the minefield or they go around the minefield into an area already under your guns.
These types of traps are not "set and forget", minefields have to be patrolled or the enemy will lift your mines and use them against you as the Australian Army found out in Vietnam.
What works for armies can work in D&D. Intelligent monsters can use traps to delay or channel movement during an encounter. A fight with kobolds is easy, unless they know where the pit and arrow traps are and you don't - they can manoeuvre so the straight path to them takes you into a trap. Once this happens a couple of times your players will move around the battlefield with much more caution.
This is up to the DM and how they have decided to implement how players go about with their investigation checks. Some checks have no chance of triggering a trap and hence don't apply to this situation, but there are a few situations where that might not be the case.
For example, if you were to check all the tiles on the floor of a room for a pressure plate you could accidentally trigger the pressure during your check as you might step on a trap during your check.
(If you rolled low enough to miss the trap)
In my experience in such cases the DM often asks how you go about doing the check and depending on the roll (if it's low enough) and your actions, you might inadvertently trigger the trap.