No Stupid Questions

As already mentioned, going from "not enough RAM" to "enough RAM" is way more noticeable than any speed difference.

If your mainboard can run two different sticks in dual-channel mode (see manual for where to put them if you have four slots, and you might have to manually configure them both to the same values in the bios) then the speed increase from dual-channel might even offset the lower frequency.

The CPU might also run some parts connected to the memory controller at different frequencies depending on RAM frequency which can also make a slight difference. But still, having enough memory is the most important issue.

I'm not a computer engineer, but I did write this comment for a question on computer architecture. At the very onset, we should clarify that RAM capacity (# of GBs) and clock rate (aka frequency; eg 3200 MHz) are two entirely different quantities, and generally can not be used to compensate for the other. It is akin to trying to halve an automobile's fuel tank in order to double the top-speed of the car.

Since your question is about performance, we have to look at both the technical impacts to the system (primarily from reduced clock rate) and then also the perceptual changes (due to having more RAM capacity). Only by considering both together can be arrive as some sort of coherent answer.

You've described your current PC as having an 8 GB stick of DDR4 3200 MHz. This means that the memory controller in your CPU (pre-DDR4 era CPUs would have put the memory controller on the motherboard) is driving the RAM at 3200 MHz. A single clock cycle is a square wave that goes up and then goes down. DDR stands for "Double Data Rate", and means that a group of bits (called a transaction) are sent on both the up and the down of that single clock cycle. So 3200 MHz means the memory is capable of moving 6400 million transactions per second (6400 MT/s). For this reason, 3200 MHz DDR4 is also advertised as DDR4-6400.

Some background about DDR versus other RAM types, when used in PCs: the DDR DIMMs (aka sticks) are typically made of 8 visually-distinct chips on each side of the DIMM, although some ECC-capable DIMMs will have 9 chips. These are the small black boxes that you can see, but they might be underneath the DIMM's heatsink, if it has one. The total capacity of these sixteen chips on your existing stick is 8 GB, so each chip should be 512 MB. A rudimentary way to store data would be for the first 512 MB to be stored in the first chip, then the next 512 MB in the second chips, and so on. But DDR DIMMs do a clever trick to increase performance: the data is "striped" across all 8 or 16 chips. That is, to retrieve a single Byte (8 bits), the eight chips on one face of the DIMM are instructed to return their stored bit simultaneously, and the memory controller composes these into a single Byte to send to the CPU. This all happens in the time of a single transaction.

We can actually do that on both sides of the DIMM, so two Bytes could be retrieved at once. This is known as dual-rank memory. But why should each chip only return a single bit? What if each chip could return 4 bits at a time? If all sixteen chips support this 4-bit quantity (known as memory banks), we would get 64 bits (8 Bytes), still in the same time as a single transaction. Compare to earlier where we didn't stripe the bits across all sixteen chips: it would have taken 16 times longer for one chip to return what 16 chips can return in parallel. Free performance!

But why am I mentioning these engineering details, which has already been built into the DIMM you already have? The reason is that it's the necessary background to explain the next DDR hat-trick for memory performance: multi-channel memory. The most common is dual channel memory, and I'll let this "DDR4 for Dummies" quote explain:

A memory channel refers to DIMM slots tied to the same wires on the CPU. Multiple memory channels allow for faster operation, theoretically allowing memory operations to be up to four times as fast. Dual channel architecture with 64-bit systems provides a 128-bit data path. Memory is installed in banks, and you have to follow a couple of rules to optimize performance.

Basically, dual-channel is kinda like having two memory controllers for the CPU, each driving half of the DDR in the system. On an example system with two 1 GB sticks of RAM, we could have each channel driving a single stick. A rudimentary use would be if the first 1 GB of RAM came from channel 1, and then the second 1 GB came from channel 2. But from what we saw earlier with dual-rank memory, this is leaving performance on the table. Instead, we should stripe/interlace memory accesses across both channels, so that each stick of RAM returns 8 Bytes, for a total of 16 Bytes in the time of a single transaction.

So now let's answer the technical aspect of you question. If your system supports dual-channel memory, and you install that second DIMM into the correct slot to make use of that feature, then in theory, memory accesses should double in capacity, because of striping the access across two independent channels. The downside is that for that whole striping thing to work, all channels must be running at the same speed, or else one channel would return data too late. Since you have an existing 3200 MHz stick but the new stick would be 2400 MHz, the only thing the memory controller can do is to run the existing stick at the lower speed of 2400 MHz. Rough math says that the existing stick is now operating at only 75% of its performance, but from the doubling of capacity, that might lead to 150% of performance. So still a net gain, but less than ideal.

The perceptual impact has to do with how a machine might behave now that it has 16 GB of memory, having increased from 8 GB. If you were only doing word processing, your existing 8 GB might not have been fully utilized, with the OS basically holding onto it. But if instead you had 50 browser tabs open, then your 8 GB of RAM might have been entirely utilized, with the OS having to shuffle memory onto your hard drive or SSD. This is because those unused tabs still consume memory, despite not actively in front of you. In some very extreme cases, this "thrashing" causes the system to slow to a crawl, because the shuffling effort is taking up most of the RAM's bandwidth. If increasing from 8 GB to 16 GB would prevent thrashing, then the computer would overall feel faster than before, and that's on top of the theoretical 50% performance gain from earlier.

Overall, it's not ideal to mix DDR speeds, but if the memory controller can drive all DIMMs at the highest common clock speed and with multi-channel memory, then you should still get a modest boost in technical performance, and possibly a boost in perceived performance. But I would strongly recommend matched-speed DDR, if you can.

Part of that is going to depend on what exactly you're doing with the computer, and how fast the other components are.

If you're just browsing the internet and want to be able to have more than 5 tabs open before your computer starts stuttering, the extra ram will be far more important than the speed.

If you're playing games, and your CPU and GPU are really good compared to your ram already, the bottleneck from the ram speed dropping may slow things down rather than speed them up.

There is no simple answer here. Usually not having enough RAM is worse than having slow ram. That being said, having 3200mhz DDR4 you might have something like a Ryzen 3000 / 5000 series cpu who are very picky about the RAM it supports. Intel is way less picky. Last time I checked DDR4 was dirt cheap. If you have a few bucks to spare you could buy a 16GB kit from the QVL of your motherboard/CPU used or new and have both the speed, the memory size and dual-channel support.

It's all a question of do you run out of memory often?

If you were going from 16 to 32GB, I'd say no. Because you probably don't max out the 16GB every day. Maybe you do. There are ways that could happen.

But with only 8GB, you're likely hitting that limit often. So yes I'd go to a slower 16GB in a heartbeat.

Yes. 16gb 2400 is faster than 8gb 3200