The two planes you list are completely different in size, let alone the adjustable mouth. The #10 is a much smaller tool than the standard block plane.

On standard block planes, I like having an adjustable mouth, as it can help when planing wide areas with difficult grain. On the smaller #102, it's not necessary, but I only use it for detail work. While I have a #102, if I were in the market for a replacement, I'd get the Veritas Apron Plane instead, as I like the Norris-style adjuster better than the L-N system. I have one of the Veritas Low Angle Block Planes and it's also a very nice tool. Again, I would choose it over the L-N based on the adjuster. Quality wise, the Veritas tools seem to be pretty much on par with L-N. They're a little cheaper, but the difference isn't much anymore, so I would pick the tool(s) that appeal to you most. Either way, you won't be unhappy.