Knowing nothing about the specifics, I'll still go out on a limb and agree with your implication that $100,000 is a big difference if it's just based on renovations and improvements.
I think I found the one house and the two you consider comps. The one at $144,500 is pretty close. It's on a slightly smaller lot, though, and the liveable square footage is 26% smaller. The one at $128,900 doesn't resemble the others at all. True, it's also a 4 bedroom/3 bath. But it was built in 2001, versus the other comp in 1860 and the house you're interested in--unknown, but it looks 80+ years old. So, the cheaper one isn't a comp.
Again, these are just wild estimates, but given the square footage and lot size, the one you're considering could be worth 20%-30% more than that other comp.
That doesn't get you up anywhere close to $250,000, though. I can't tell from what's online what renovations were done. But a total renovation of that property might run $60,000, +/- about 15% in many areas of the country. And even that wouldn't get you up to $250,000.
So, my uninformed comment is that, from what I see online, I wouldn't be surprised if the house you're looking at ends up selling for significantly less than its asking price.
Best thing to do is ask your Realtor to run a CMA. If you don't have a buyer's agent, you should get one. Or at least ask one for a CMA.
One other thing to consider is whether the community prices would support such a spread on resale. Looks like houses in the area are listed for roughly $120,000-$170,000. The community may not support a home price of $250,000, regardless of the quality of the repairs and renovations.
But a local Realtor can provide much better, more informed advice.
Hope that helps.