I understand the traditional difference between the 7400 series and the 4000 series logic ICs, but since there are CMOS versions of the 7400 series, is there an advantage to use the 7400 CMOS version over the 4000 series chips? Please note I'm not talking about TTL vs CMOS, as that has been discussed thoroughly before. If there is no difference (read significant difference), I'm assuming then that they would be able to interface with each other? I would think the voltage levels for high and low for both CMOS versions would be near identical, but please correct me if I'm wrong.
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