Generalizing comparisons for 20% vs 25% down

[Doug Durgee]

I currently have an offer in on a place and am trying to select between financing deals. One bank is pushing for 25% down, which in this case will give me 3.25%/30 years. The other is quoting 4%/30 years for 20% down. The difference in down payment is about $10K, and the difference in monthly payment is about $150/mo., which I think tells me 25% down will pay off if I keep the house for more than 5.75 years ($10K/($150*12)). 

Am I calculating that correctly? I ask because if I drop the rate on the 20% down option to say 3.8%, the difference in monthly payment drops to $120/mo., which would yield 6.9 years in the equation above and look worse in comparison despite being the better rate. Is there a proper way to evaluate the difference here that I'm missing?

I'm looking more for appreciation/net worth than cash flow/income replacement on this one, so I'm leaning towards the 25% down deal. More than that though, I'd like to know how to properly generalize this so next time I can let the numbers decide. I wanted to just throw it into an equation, but maybe there's a set spread or something else that works (e.g. for 25% down to work, the rate has to be X points better to make sense). Suggestions?