It's not the disc drive. (They both use bluray. So does the Xbox 1 for that matter...)
The problem is the design of the system and how they're coded. The PS3 uses a vastly different set up it focused on a 6 core processor (each at 3.2ghz) with a 7th master (also at 3.2ghz) that provided all the instructions to each of the others. This means coding for the system is much more difficult because each instruction has to be routed through one main processor. (When done properly this means a greater speed/power... but when not done it means games run like crap.)
The PS4 on the otherhand uses an x86 architecture which is basically just a standard PC. It has 8 cores with 1 dedicated to the OS. The other cores are for the games. This means a huge difference in how games are programmed. Any of the remaining cores can do any of the tasks. They don't have to be routed through one processor and scheduled. This is important because it means that technically more can be done because it doesn't need to rely on that one core.
So then why can't the PS4 emulate the PS3?
Because software emulation requires an order of magnitude more power. The PS2 has a 333mhz processor. It takes at least a dual core processor at 2.4 ghz per core to emulate it. The PS3 would require somewhere within realm of a 32 ghz (per core) octa core processor to completely software emulate that. The PS4 does not have that level of processing power. This is why they can't emulate it. They would have to recode the entire game from scratch to get it to work on the PS4. (Which is what they're doing for remasters and collections of games from the PS3...)
They could easily include the cell processor in the PS4 but it would increase the cost of the PS4 (probably within the range of $60-$80) like they did on the PS3 initially to make backwards compatibility with PS2. But this means sacrificing the cost advantage they had over Microsoft. (Kind of a moot point now, but it's unlikely they'd want to make the hardware even more expensive later in it's life cycle.)