Take 10 and Take 20 are two different things, so I'm not sure how you could compare them.
Here is a short analysis of the skills needed to detect and conceal objects and creatures.
There are 3 categories to consider:
creature or object
moving or unmoving
<10' away or >10' away (you can Search for something < or equal to 10' feet away, but not farther)
for each category, which skill is used to conceal and which is needed to detect the thing is question?
(moving/unmoving) (creature/object) (<>10' away)(skill to conceal/detect)
moving creature <10' away: Hide, Spot
unmoving creature <10' away: Hide, Spot
moving creature >10' away: Hide, Spot
unmoving creature >10' away: Hide, Spot
moving object <10' away: none, Spot
unmoving object <10' away: none , Search
moving object >10' away: none, Spot
unmoving object >10' away: none , Spot
You use Spot to detect all moving things.
You use Spot to detect all creatures.
You use Hide to conceal all creatures from view.
There is no skill for concealing objects from view.
You only use Search to detect unmoving objects that are <10' away. You don't use it to detect unmoving creatures. You don't use it to detect unmoving objects farther away than 10'.
This is not consistent because an unmoving creature is essentially no different from an object of the same size and shape, yet there is a different skills set associated with each one.
You can visually Search for something in a square 10 feet away from you, but you cannot Search for anything farther away than that, even though it is possible to see farther than 10 feet.
Hide is popularly used to conceal an unmoving creature from sight, but the skill description says that the skill is normally used with a move action.
An easy way to make the system consistent would be to get rid of the Search skill. Use Spot for both detecting stealthy creatures as well as traps. If you hide an unmoving object, including yourself, in a place that has less than 100% concealment, use an Intelligence check to determine the Spot DC. You could take 20 on this check. In order to find something with 100% concealment, a PC has to describe looking in the right place.
A complicated way to make the system consistent would be to use Search for all conscious detection and Spot for all unconscious detection. You would use a Search check to determine the Search DC for when a character hides an unmoving object, including himself. In essence you are Searching for the best hiding place, and thus could take a 20. You would use a Hide check for when a character moves stealthily. You could use both Search and Spot from a distance with a penalty. It would be easier to detect an unmoving object with Search. The chance to detect an unmoving object with Spot would be equal to the Search DC plus 5. Thus anyone could detect a secret door (Search DC 20) by making a DC 25 Spot check (elves would in essence get a +3 racial bonus on their chance to Spot secret doors).
You would determine the Search DC for traps and secret doors through some use of Craft(trapmaking) and Profession(architect) checks. Maybe: Hide a door in a structure with Search DC 20 - Profession (architect) check DC 15. Create a hidden trap with Search DC 20 - Craft (trapmaking) check DC 15.
Edit: things don't line up the same in the actual post.