I am looking to get my first road bike and I am deciding between a 23.2 pound road bike with a minimum gear ratio of 34-32 or a 20.7 pound road bike with a minimum gear ratio of 34-28 and I was wondering which bike would be easier to climb with.
Lower gearing (or gearing in general) is generally more important than the bike weight for climbing (for most riding as well, sans high level racing). Both of the gear choices are pretty low and you'd need a pretty steep hill (or towing a lot of cargo) in order to need the lower gear over the slightly higher lower gear. As Criggie points out, there are other factors to consider other than weight -- ergonomics, build quality, etc. which can have a more profound effect on how you ride.
A difference of 2.5 pounds is easily within the fluctuation range of your weight over the course of a few days, and is likely on the order of a percent or two of the total bike+rider weight anyway so you can basically ignore it.
As the comments say, you can switch your gearing in the back fairly easily, but this may require a new derailleur depending on capacity and cog size limits and a new chain (this is a relatively easy replacement). Note that you have to give something up for a fixed number of cogs and different gearing combinations (such as the spacing between shifts, max or min gear). So, if the largest cog is 32 in one case and 28 in the other and they have the same smallest cogs, you'll likely have bigger spacings between shifts on the larger cog one. Ideally, you'd try them out and see what you like better.
Maths says that one bike is 11% heavier and has a low gear ratio of 1.06:1 whereas the other bike is 1.21:1 So both gearings are quite low already.
The lighter bike will be "easier" for climbing, but not so much you'll notice. There are many other considerations like comfort and quality too.
Example I changed from a 26/24 to a 26/28 and my strava climb for a 19% grade went from 1 min 59 to 1 min 57. Not a significant change, and that could have been down to wind or motivation or anything.
The answer to both parts of you question is yes. Climbing is easier with a lighter bike, and easier with lower gearing.
But several factors that you don't mention interact to determine which bike is better for you. These are your weight, how steep the hills you'll be climbing are, how strong you are, how hard you want to work, and how the bike fits you. And maybe I've left some factors out.
Firstly, consider some simplified physics. You use the cranks, chain rings, rear gears, and rear wheel to essentially lever your weight and that of the bike up the hill.
If you weigh, say 150 lb (68 kg), and carry 2 lb of water (about 1 kg), the total for the first bike is 175.2 lbs (79.6 kg) and for the other bike it's 172.7 lbs (78.5 kg).
Now we use those levers. Since everything else about the bikes is same, we only need consider the lowest gears - 32 on the first bike, 28 on the second.
For the first bike, divide 172.7 by 32 gives us 5.4 (lbs per tooth, for those who like units).
For the second bike, divide 175.2 by 28 gives us 6.3 (lbs per tooth).
So we see that the gearing dominates the result. The bike with the lower gearing will feel about 15% easier when climbing a hard hill, even though it's the heavier bike.
The next question is: will you actually use this lower gear?
What happens when climbing a hill is that your strength (how hard you can push the pedals) multiplied by your cadence determines the power you produce. It's your power output that gets you up the hill, and since your strength is limited it's your cadence that determines your power output.
Assuming we have a maximum steady power output, then as the hill gets steeper, our cadence (and road speed) drops. We change to a lower gear at that point, until we run out of gears. Until this point we have been able to produce our maximal power, but now that the hill is steeper we don't have enough strength to keep turning the pedals that fast. So our cadence, road speed, and power output drops away.
So if you're strong enough and the hills you climb are not too steep, then you will not need that lowest gear. That's why the Pros don't have granny gears - they are strong for their body weight. But for most of us, that lowest gear will always get some use.
Is it worth putting lower gears on the lighter bike? Firstly, will they fit, or will it be extra expense? If the lighter bike costs the same (unlikely) and the lower gears fit, then go for it.
Finally, which bike fits you best? There is absolutely no point in getting a bike that does not fit you properly. A poorly fitting bike can quickly lead to pain and injuries.
There are also few factors other answers omitted
quality of every single part of bike will make difference too, there is a lot of points where friction makes difference and it can really make a big difference
We can safely assume that two bikes you are comparing are about the same quality meaning about the same friction of parts
Different frame types makes you ride in different positions and that makes you move slightly different parts of muscles.
I recently dropped my old, completely broken mountain bike and got much more comfortable trekking one with everything working smoothly. And yet position difference makes it harder to climb steep hills, it's just harder to push on pedals this way.
You mentioned that both of them are road bikes, but that doesn't mean both are exactly he same, there still might be noticeable difference in proportions leading to noticeable difference in climbing