Simplified and barebone comes to mind regarding the new system. The old one wasn't perfect, far from it, but it felt more natural somehow for me. With some work and overhaul, I would prefer the old system which was more suited for RPG in my view. However, In reality, there isn't much difference between the two systems when it comes to actual skills. They are both still using the 25/25/25/25 system more or less when it comes to weapon skills and utility skills that requires a certain skill level to attempt (hacks and lockpicks etc.) altho FO4 have fewer steps in some of them, more in others and FO4 gates them behind levels. Gating skills behind levels only mean that they (e.g. Bethesda) have an easier time balancing the game, at the cost of player freedom. Who's to say my character wasn't a highly regarded specialist in computers from the military? Well, gating says so.
Former system didn't have level gating of skills, which were actual skills, only the perks. Whereas in FO4 perks becomes skills. Dunno why they didn't just call them skills, since that is what they are in function in FO4. Perks in FO3 / NV was a bonus thing, that helped shape your character further. In that regard FO4 is a real lackluster for me, since skills in FO4 is only that. No skill / SPECIAL requirement for using certain weapons effectively nor for armour. So while the old system let you have 100 science with 1 int, the new system let you wield a minigun with 1 str as if it was natural, and you are a computer genius with average int. FO4 also have have some weird perks / skills to say the least, where at least half of them, you wouldn't consider them as first picks, ever.
None of the two systems are perfect, but in my opinion, the old one had far more potential with some tweaking, to make choices makes sense.