The most simple yet important aspect of any weapon is it's damage. The M4A4 and M4A1-S share similar damage values, though they vary slightly, especially at range. This table explains the amount of damage that the weapons do at point blank range.
Both weapons do identical damage at point blank range, and both are capable of one shot killing an unarmored opponent, and can kill an armored opponent with one shot to the head and one shot anywhere to the body. However, this damage changes at range. The M4A4's damage drops by 1% per 500 units(it takes 1 second to run 250 units, so 500 units is 2 seconds of running distance), while the M4A1-s drops by a whopping 3% per 500 units. So when it comes to long cross map shots, such as from the back of A site to Catwalk on Mirage, the M4A4 wins this one.
Rate of Fire
Because the two weapons have such a similar rate of fire, this number is relatively insignificant, but it is still worth noting. The M4A1-S fires at a rate of 600 rounds per minute, while the M4A4 fires 666.67 rounds per minute. This difference is quite minuscule, but it may have an impact in extremely rare scenarios.
This next topic is a topic of great discourse among the CS2 community. The M4A4 costs $3100, while the M4A1-S costs just $2900. Although this is a difference of just $200, it matters a lot in the round after winning a pistol round, where you may not be able to risk spending your entire bankroll on an M4A4 and head armor.
Nearly as important as a weapon's damage is it's ammunition capacity. If you have yet to master spray control, then ammo capacity is a vital factor in deciding between these two weapons, and they have quite the difference. The M4A1-S holds just 20 rounds per magazine with 80 rounds in reserve, while the M4A4 has an additional 10 round per magazine and 10 extra rounds in reserve for a total of 30 bullets per mag and 90 in reserve.
Recoil plays a huge factor in CS2, so you must consider it when choosing between the M4A1-S vs M4A4. The M4A1-s has a much easier spray to control, while the M4A4's bullets spread out much more and require high level spray control.
Overall, the final decision comes down to you. If you are good at spray control and aim, and value the ability to hit long range shots, then the M4A4 is your best option. If you are newer to the game, you may want to try the M4A1-S due to it's easier to master spray control. Then again, maybe the most important thing to you is skins, and if so then check out these amazing affordable skins for the M4A1-S and M4A4!