If you have a piano that is more than three decades old or a newer piano that has been used heavily, it can almost certainly be improved by replacing its hammers and perhaps action parts, damper felts, various bushings, and strings. A vintage piano may require a more comprehensive treatment, including modernizing its touch, replacing the pinblock, and addressing definiciencies in the belly by repairing or replacing the soundboard. And a pre-modern piano may require some level of redesign and structural re-engineering in order to meet modern expectations for performance and stability.
The difference between rebuilding and restoration is the difference in goals: whereas a restoration aims at reproducing the manufacturer's original intent, a rebuilding treats the instrument as having the potential to meet modern pianistic expectations. Although we can restore any piano to its original specifications, I see the rebuilding of American grands built after about 1880, and of all modern European grands, as a less expensive—and sometimes superior—alternative to buying a new piano.
Read more about the differences between restoration and rebuilding.
I realize that different customers have different needs. If you aren't sure about the tone or touch you want, or why you like a particular piano so much, don't worry. It's my goal to identify your preferences by observing your playing style, your repertoire, and your reactions to the touch and tone of your and other pianos. Although a modern concert grand will never sound like an intimate, quiet baby grand and vice versa, each piano's character can be adjusted to a surprising extent. I suggest that you try as many pianos as possible and form opinions about them so that you can better communicate your preferences to your rebuilder.