These two locations offer very different experiences, making it hard to directly compare them. Your choice will really depend on the type of experience you're seeking.
Merligen is a very small village with fewer than 1,000 residents, while Neuchâtel is much larger, with a population of around 45,000—similar in size to Thun, which is about 30 minutes from Merligen.
Because of its size, Merligen has fewer restaurant options and amenities, but it more than makes up for it with its stunning location. The village sits right on the Lake of Thun, with the impressive Niesen mountain (known as the Swiss Pyramid) directly across the water. The views are often breathtaking, especially in the mornings or during a beautiful sunset. I have sometimes gone past on the bus, and always enjoy the view.
From Merligen, you can easily take the funicular up to Beatenberg (20 min away) or continue on to the top of Niederhorn mountain (40 min). Nearby attractions include the St. Beatus Caves and the hanging bridge in Sigriswil. You can also take a boat or bus to Thun to explore, or head in the opposite direction toward Interlaken. Along the way, you might stop in Unterseen, where there’s a lovely restaurant on the lake and a bird sanctuary at the Neuhaus bus stop (18 min). From there, you can continue on to Interlaken and explore many more areas from there.
I think that this would be a very tranquil, more out of the way location, but still close enough to lots of exciting opportunities.. Sandoz has provided a great overview of Neuchâtel—now all you have to do is decide :-)
Either way, you can’t go wrong.