74LS vs. 74HC series ICs for Ben Eater's 8-bit Computer
There are 5 primary differences between the 74LS and the 74HC series. Speed is not one of them, as their upper limit is about 20 MHZ in terms of clock speed.
They have the same pin outs for both DIP and SOIC packages, so that is not an issue. They are both considered 5 volt devices.

Many issues do stand out. 


Logic threshold voltage.
Power consumption.
Input impedance.
Output drive current.
Output drive voltage.


INPUT VOLTAGE

The input voltage for the LS and HC series is close, but the HCT series mimics the LS series in terms of a '1' input and a '0' input. 74HC needs more voltage to be considered a logic '1'. Both types have a no-mans land of about 2.5 VDC where it is in a linear mode and may oscillate.

INPUT IMPEDANCE

The 74HC series has a very much higher input impedance than the 74LS, which actually 'leaks' a small positive current out of an input pin. It is in the uA range so normally is not an issue.

OUTPUT DRIVE CURRENT

The 74HC series has an output drive current of +/- 25 mA, so with a resistor it can drive LED's directly. A 330 ohm to 1 K resistor will cover most LED's except the "high-powered' types. The 74LS can sink a couple of mA and source about 1 mA at most.

OUTPUT DRIVE VOLTAGE

The 74HC outputs swing rail to rail, even with a 15 mA load to either rail. The 74LS series can sink an output close to ground voltage, but can only source Vcc-1.2 volts due to its bjt outputs. It is very common to see pullup resistors on both the 74HC and 74LS data and address lines to prevent floating if nothing is driving the bus, but the 74LS series used them to help make logic '1's closer to the Vcc supply rail.

CURRENT CONSUMPTION

The 74HC/74HCT series also consumes MUCH less current, just a few uA in a static mode. The 74LS consumes 1,000 times as much idle current.

OPTIONS

There is no reason to use the 74LS series except for legacy reasons. Even so, replacing some with a 74HC/74HCT series will reduce power consumption a great deal. The 74HCT is a better match to existing 74LS logic in terms of input threshold.  For faster logic the 74AC series is good to 120 MHZ, the limit of the 5 volt 74ACxx, 74HCxx, 74HCTxx logic series. The 74HC/74HCT/74AC series is still in production by several manufactures, while the 74LS is going the way of the Edsel. You may find them on Ebay. There are 5 volt ECL/PECL logic IC's but that is not what this post is about.

LINKS

The data sheets are too long to include all of them here, so I picked the 74xx74 flip-flop as a common example. There is no guarantee these links will last for decades.

http://www.ti.com/lit/ds/symlink/sn74ls74a.pdf

http://www.ti.com/lit/ds/symlink/sn74hc74.pdf

http://www.ti.com/lit/ds/symlink/sn74hct74.pdf

http://www.ti.com/lit/ds/symlink/sn54ac74.pdf