A lot could be written in response to your question and I’ll try to limit it to the essentials.
180 gram vinyl does not necessarily sound better than vinyl of more standard thicknesses. I would qualify the above poster’s statement that other factors have more importance ("everything up to the point of actually stamping the vinyl") to state that ALL factors can have an important impact on final sound quality.
Also, some people run cartridges that are very sensitive to vertical tracking angle ("VTA"). If VTA is not easily adjustable for such cartridges and therefore not adjusted for the thickness of each LP, then sound quality will depend to some extent on whether VTA, as set up for that cartridge in that arm, favors standard thickness LP’s or thicker ones.
As for the general question of whether 180 gram pressings sound better, there is a temptation to assume that if the reissue house is pressing on 180 gram vinyl, it must be a good pressing - not necessarily. LP’s pressed prior to 1980 are all-analog (i.e., the sound was never digitized at any step), many of them are incredible, and they can beat the pants off of 180 gram reissues that are not carefully done. Also, a lot of 180 gram reissues are pressings of digitized music - generally speaking, if the recording took place at any time after 1982 or so, there is an excellent chance that the music was digitized at some step of the production chain (with few exceptions, everything after about 1990 is digitized). Unfortunately, once the music is digitized, the damage is done. It is therefore important to look for evidence that the 180 gram reissue is "all-analog" - the good ones will often describe the entire chain: recording, mixing, mastering, pressing.
I have been hinting at the answer to your final question, which was not very clear to me, but I think is basically whether a 180 gram LP (or other high-quality LP pressing) will sound better than a CD, i.e., what sounds better, vinyl or CD’s? This question creates an enormous number of emotional posts in audio forums, but I’m going to give you the answer - generally speaking, a 16 bit / 44.1 kHz. digital recording played back on a high quality CD player or music server is inferior in sound quality to a reasonably good condition vinyl LP assuming a decent vinyl playback system (i.e., a "Rega Planar 3" level table with decent cartridge that is set up properly and run through a decent phono stage). The biggest problem with 16 bit / 44.1 kHz. digital music is the inability to get high frequencies right - simply put, sampling a piece of music that occurs at frequencies above 10,000 Hz. or so only 44,100 times per second means that much of the waveform of the music is being missed - put in really basic terms to aid understanding and assuming a 10,000 Hz. signal, "pictures" of the music are taken by 44.1 kHz. digital only about four times (10,000 ÷ 44,100): a quarter of the way through the oscillation, half way through, three-quarters of the way through, and at the end, but none of the movement in between is captured. It’s not an exact analogy, but just like the experience of watching an old film begin, whereby you see the first few individual frames scroll by as the movie reel comes up to speed and it doesn’t seem like a movie - you can see the individual frames - 44.1 kHz. digital doesn’t move fast enough to record the entire waveform and you are just hearing small parts of those frequencies. Put another way and again analogizing to sight, taking normal video of a bullet traveling will not show the bullet because it is moving too fast to be captured by the video - high speed video, on the other hand, will show the entire flight of the bullet. So high frequencies are like the fired bullet. 44.1 kHz. is fine for lower frequencies, because low frequencies oscillate slowly enough that sampling them 44,100 time per second is going to capture the vast majority of the waveform - using the example of a 700 Hz. midrange frequency, taking 44,100 photos per second of something that oscillates only 700 times per second means that you’re going to capture almost all of the oscillation. This is why symphonic music, which features a lot of string instruments having very high frequency harmonics, sounds weird and wrong through 44.1 kHz. digital, and why all-DSD digital (i.e., SACD) sounds so much better than regular digital and more like analog - the sampling rate is high enough to more or less get high frequencies right.
The superiority of analog over digital is not a controversial point among experienced audiophiles, which is to say, those people who have ample experience with high resolution systems and well set-up turntables using decent cartridges. Does a scratchy record on a bad pressing of a given performance sound worse than a 16 bit / 44.1 kHz. CD of the same performance? Sure. But assuming reasonably clean vinyl on a properly set up table, especially with music having any real high frequency content, this is a settled question.