Remodel
Choosing to remodel is the perfect solution if you love your current location, your landscaping, your neighbors. You just don't want to give that up, but a newer home would be nice. Let's think Old-to-New. What would you change about your home if you could? What things are most important to you? What would your "new" home look like if you could change a few (or a number of) things?
The benefits of remodeling are not limited to just making yourself happy. An updated home increases in market value. That means when you are ready to sell this home and move on to the next, you are selling an updated home that typically nets a better price than one that is not presentation ready. It is typically time and money well spent.
Renovate
The house you have been admiring across town finally went on the market, but when you step inside you realize it needs work. Still, it calls you to come home. Renovation can be the solution. It almost seems like remodeling on steroids because in many cases you are updating things throughout the house, not just making cosmetic changes. The awesome thing about renovating a home is that in many cases you are bringing back the character of the home's previous life, but doing it to today's code standards. It's amazing, it's fun, and it's worth the experience if the house had a good start in life.