Should I buy 2003 Yukon XL 2500 with 3.73 or 4.10 axle?

I currently own a 2003 1/4 ton Yukon XL 4x4 and will be purchasing a travel trailer, hence the need for more towing power of the 3/4 ton version.

There are a few choices when it comes to the 2500 and I'm wondering how much difference there is between all the options.

There is a 6.0 L that comes in both the 3.73 and 4.10 ratios and can tow 7,600 lbs and 9,600 lbs respectively. (per the owner's manual)

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quick tangent here...my 4x4 1/5 ton 5.3 litre, according to the owner's manual, is capable of towing 7,100 lbs. But I rented a travel trailer few years ago which fully loaded was at about 6,000 lbs and my 1/5 ton was getting "owned" by the trailer on regular flat city streets. Travelling up I-80 from Salt Lake to Park City (Parley's Canyon)--a very steep grade--I was struggling at 25 MPH and the engine was downshifting like crazy.
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There is also a 8.1 L that comes in the 3.73 and 4.10 ratios and can tow 10,100 lbs and 12,000 lbs respectively. (per the owner's manual)

My initial thought is that I want the most power available so I figure it's best to go with the 8.1L and ideally the one with 4.10 ratio because it can pull 12,000 lbs. Would I see or feel much difference with the 8.1L with the 3.73 ratio?

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tangent #2, I'm finding 8.1L for sale on the internet but most seller's don't know that the axle ratio is. Is there a way for me to run the VIN and find out what the gearing is? I also know there are RPO codes in the dashboard that may reveal what the gear ratios are but most sellers are posting RPO codes on their online listings...
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I'm almost ruling out the 2500 6.0 L because it's only rated at pulling 7,600 lbs...a mere 500 more pounds than my 1/2 ton.

Am I missing something or would I see a really big towing difference in an additional 500 lbs of towing capacity between the 2500 6.0 L and my 1500 5.3 liter since, per the owner's manual, the 2500 is rated at pulling an additional 500 lbs?

Any responses would be much appreciated

as far as the axle ratio goes, you'll want as deep as you can afford. if you can get by with a 4.10, i'd go that route, but of course your non-towing time will also be affected.

towing with the 5.3l and a fully loaded travel trailer will leave some desire for more performance, especially with any higher grades involved on the route as you're basically maxing out the capacity of the 1500 platform.

Thanks for response

Thanks for the response, it's much appreciated.

VINs won't tell you axle ratios, only the RPO codes will. If the vehicle in question is still owned by the original owner then its likely they might still have the window sticker which will also list the gear ratio.

The 2500 no matter the drivetrain will handle the weight a lot better than any 1500. The 5.3 and 6.0 both like to rev and that shocks some people when they are winding out but that's par for the course. The 8.1 is a whole different beast and makes gobs of lower end power. It'll pull down a house, but you'll be lucky to get 11-12 mpgs unloaded. Loaded you're going to be in single digits. It really depends on how you're going to be using the truck more, if towing majority of the time then go 8.1, if not get the 6.0.

Now thinking swapping out 3.73 for a 4.10

Thank you so much for the responses everyone has given so far, it is nice to know there are people out there willing to help out

After many fruitless searches for the perfect vehicle, we like upgraded models leather, etc. we are now considering swapping out the gears.

Based on the research I have done, I believe both front and rear axles need to be replaced to 4.10

While I understand the 3/4 ton models have suspension and other features that are more complementary towards towing, what would be the practicality of me upgrading my 1/2 ton with a 4.10 ratio?

In other words, how many more pounds of towing what I gain by just swapping out my axles?