So, according to the wiki page on Ba Sing Se it is "one hundred meters tall." I cannot find any source for this. I cannot find any reference even to "meters" at all in any of the episode transcripts found here. In fact, I could not even find the height of Aang or any other character. This thread provides some numbers, but even the author admits to its statistical improbability. So I think it's safe to say that there is no definitive way to measure such things, simply because there are next to no definitive convertible measurements.
So what answer is available? Ratios to guessable heights, particularly the height of two wall sentries and the cabbage merchant. Standing all around the same height, I think it is reasonable, or at least necessary, to assume that the three men are of average height. In this picture from S02E35 (The Tales of Ba Sing Se) the cabbage merchant is 12px high, and the wall is 660px. So the wall is 55 times the height of the average man. Using a Wikipedia article linking to the defunct url of a 2012 study, the average height of Chinese men (since ATLA is based on Chinese culture, I thought it appropriate to use Chinese stats) is 167.1cm, or 5.5ft. This makes the height of the wall 92m, or 302ft. Of course, there is no guarantee that the height of the cabbage merchant is anywhere near that number, but I think it is the best we can do. One could also try measuring the height by comparing it to that of the boulder team Avatar rides up the side of the mountain in S02E33 (The Drill), or the height of the Fire Nation tanks and the Fire Nation Drill. Furthermore a more accurate height measurement might be found by sourcing height data from a time period more comparable to ATLA's.
To extrapolate the width, I first used this picture from S02E33 (The Drill), identifying the height of a standing soldier in the background to be 240px, and the height of the pier to be 560px. The width of the pier is 200px. So the height of the pier is 7/3rds the height of the man, and the width 5/6ths. Moving on to this picture from S02E33 (The Drill), each pier in the lower guardhouse is 45px high by 13px wide. The wall in front of the guardhouse (ignoring the protruding parapets) is a line moving 344 pixels on the x axis and 25 on the y. Using the distance formula, this means the wall is 345px wide. Using the height of the pier for the translation, we get a ratio of 161/9, or 17+(8/9). Using the width, we get a ratio of 1725/78, or 22+(3/26). Using yet another method, each pier in the middle guardhouse is 15px by 5px, whereas the wall is 105px wide. This leaves us with ratios of 49/3 (16+(1/3)) using height and 17.5 using width. As you can see, the ratios are not uniform, likely due to many things including inaccuracies in my measurements, inaccuracies due to the low resolution of the video, or simply incorrect ratios drawn by the artist. But the middle guardhouse gives us ratios somewhat similar, so let's use those. Since the mean is 16+(11/12), let's just round that to 17 and say that the width of the wall is about 17 times the height of a soldier. Using the same real-world measurements as before, 167.1cm or 5.5ft, we get 28.5m or 93.5ft for the width of the wall.
Given that the wiki page gives one hundred meters for the height, and the measured width of the wall is quite near 3/10ths of the measured height, I think we can rather safely assume that the wall is intended to be about 100m high and 30m wide.