All those Perks are still there.
You just get a rank of the Science perk instead of increasing your science skill.
What is the purpose of skills?
To let your character be better at things than you.
To differentiate between characters and NPCs.
If your character has a high guns skill then he will have less spread and recoil than a character or NPC that has a low guns skills.
If your character has a high melee, then your character should hit better with a sword and do more damage with the sword than a character or NPC that doesn't have the skill.
What does a Perk do?
It provides an in game benefit that other characters and NPC can't do if they don't have the perk.
For example letting a trained archer zoom in with his bow.
Or letting someone know how to use Power Armor (that sounds like a skill).
They also better define a person's ability.
Maybe a person is great at throwing a grenade or maybe they were great at whipping up some homemade explosives.
Looking at it that way, there is not much difference between perk and skills except perks are more specialized.
Percentage skills worked great for F1 and F2, but most modern games have trouble using them.
Perks on the other hand can do a variety of things, are a lot easier to explain, and provide more customization than just having a 100 in a general skill.
So to get better with a weapon, you need to take the perks that cover using that weapon.
Perk that might reduce recoil or allow you better headshots in Vats.
To get better at hacking you take more ranks of Computer Wiz.
So pretty much the same thing.