7400 series CMOS vs 4000 series logic IC

The difference depends on your system definition. On the one hand, 74HC operates over a limited voltage range, with 6 volts specified as the maximum supply voltage. The CD4000 series, on the other hand, is rated to a maximum of 18 volts, so it may well be easier to use the CD4000 series in a battery-operated system.

If the limited voltage range of the 74HC line is not a problem, the line is much faster. For instance, comparing the CD4011/74HC00 (Quad 2-input NAND gates) gives propagation delays at 5 volts of 90 nsec (typ) vs 7 nsec. For the CD4063 vs the 74HC85 (4-bit magnitude comparator) the numbers are 625 nsec (typ) vs. 63 nsec. The CD40192 4-bit up/down counter has a typical count frequency of 4 MHz, while the 74HC192 goes at 36 MHz.

It's worth keeping in mind that both lines run faster at higher Vdd, so a CD4000 at 15 volts will do better than the numbers here, but the order of magnitude difference is not erased.

And yes, the 74HC series is designed to roughly maintain the speeds of the 7400/74LS00 lines, and often allows drop-in replacement for much lower power.

HC7400 runs 2v to 6v supplies (partly TTL compatible)
HCT7400 (fully TTL compatible) runs 5v +/- 0.5v supplies
4000 series runs 3v to 15v (recommended VDD)

so with 5v supply, 4000, HCT7400 and HC7400 are fully compatible

7400 is comparable speed to TTL
4000 is significantly slower