I have done both things, and both have their challenges. In established neighborhoods it is common to have deed restrictions, city codes, and historical districts which might prevent you from tearing down and rebuilding a home—even if it might look the same on the outside once the work is done. Even if you are able, you lose all the benefits of being grandfathered into older building codes.
When I “renovated” the house I live in now, I was forced to meet or exceed current building, seismic, and zoning codes because I added 25% or more livable space. (Another thing to consider—many older properties, even larger ones might have very small rooms rather than open floor plans because they were built before floor and roof trusses were used and the spans were designed to be short [often leading to long narrow rooms across a bigger home] spans of no more than twelve feet (12’-0”) because that was as long as affordable joists can span. It is also possible some entity might restrict remodels to materials and methods that match the existing—but it seems those kind of historical societies wouldn’t have the power to make their rules stick; but they might just make the approval process hell for you. Again, even if you can use modern glu-lam beams to open up spaces—you will have to retrofit huge footings to support the posts that support the beam that replaces a bearing wall. The weight of the structure and its contents remain the same [live load and dead load], but now instead of being supported by a twenty or twenty-five foot long wall— it must be supported by one post at each end. That large load transfer still needs to be supported.) As a result of meeting current codes, I was forced to add ten thousand dollars worth of water retention to the property (underground tubes with holes drilled in them every eight inches or so in every direction in a bed of 2” to 5” river rock gravel wrapped in landscapers fabric to keep soil from settling into the gravel and diminishing the leaching property of it. I also had to create surface ponds that will hold rain water during a downpour. The total of these water retention measures are 80% of two hours of the worst precipitation ever recorded in the last hundred years—in my case 175 acre feet of retention before one drop of rain from my property runs into the gutter [where 100% of my neighbors rain water goes and where all of mine used to go]. After meetings and applications for variances- and endless calculations and agreement from the city civil division that this was wrong and unfair, all variances were denied. The only way to avoid that expense was to build exactly what was there before.) I was able to get the city to strike down the requirement that I jackhammer out the entire four foot wide (4’-0”) sidewalk and replace it with five foot wide (5’-0”) sidewalk because in the middle of the block where no one else was likely to renovate to the degree they would have to pull a permit made little sense. There would have been seven hundred feet of four foot sidewalk- then one hundred feet of five foot sidewalk- followed by eight hundred feet of four foot sidewalk—variance granted, saving me another $3,500-- $5,000.
I would have upgraded the plumbing and electrical anyway—but certain modern circuit breakers are VERY expensive added about two-thousand dollars to the overall cost. Another matter is that many jurisdictions (most I believe) require electrical wire to be pulled by a certified electrician. There are those who will sell you their stamp and signature if they just inspect what you have done yourself—but mostly if you are going to rewire more than just a run here and there it is worth paying them. I worked on a vacation home where the homeowner and his buddy insisted on pulling the wire themselves. Every single circuit was a homerun (ran all the way to the box); after several weekends working on it the inspector red tagged it because she (yes, a woman inspector at the county office!)knew it wasn’t pulled legally. The electrician with the cert. (not an electrical contractor, a guy who was certified) pulled out all their work and rewired the thing. He was smart enough to add outlets and switches where they would do good, and delete the ones that were useless. He used half as much wire and the owner was left with enough copper to wire a huge garage and shop with living quarters above.
One big problem with “renovation” is that most people think of surfaces when they think of renovation. Putting granite countertops into a house designed and built before the war will give you an outdated design and impractical house little suited to modern living - - - with granite countertop! In Pennsylvania and Ohio, I saw any number of hundred year old houses with various (horrible) “updates” incorporated. Many of those were designed before indoor plumbing so when they tore down their outhouse, they converted the smallest bedroom into a bathroom; usually meaning ONE bathroom for the entire household. Certainly no master suites with luxury bathrooms and walk in closets right off the master bedroom. If you want old fashioned charm, share a bathroom with your kids. The charm tends to wear off pretty quick. But this whole post to say it is best to consult a design professional before starting on any renovations. It is SO MUCH better to start with a workable modern space plan—then try to see how the perspective property can best be altered to achieve your goals. Then you know going in you will have to sacrifice D, E, and everything after H; but you CAN have A, B if you are willing to pay and sacrifice F and G, and C for sure. It goes a long way toward being happy with the end product. It also allows you to do what you can afford now—and put some stuff off for later knowing what and where it is/will go. You can pre-wire and pre-plumb for future projects with a LOT less cost if you know this storage area will be a Jack and Jill bathroom once you have toddlers. Design professionals also know about setbacks and other restrictions (after a certain number of toilets, every pipe in a house has to be larger even if they don’t attach to a toilet for example). It also saves the buyer’s remorse of having an idea occur to you after it is too late. A design professional will ask you questions that would not occur to you until you are finished with the remodel and living there. That is why successful designs are built over and over.
To summarize, unless you plan to rehabilitate, get input from a design professional before starting any home improvement project. Even if you just plan to rebuild and repaint what is already there, it will still be harder and more expensive than you think. If you actually renovate and change things- - - there is a very good chance you will end up doing the wrong thing in the wrong place, and do it poorly.
NOTE: I wrote twice this much, but you don’t need all those examples, so I cut it back to this.