Smoothness right out of the box. Easy to read scales. Dead accurate for machine set up (e.g., blade stops/fence stops/tilting bed stops, etc.). It's kind of like using a L-N plane vs. a new Stanley plane... you see and feel the difference.
They make them with scales in 64ths and they have what they call "quick reading" 32nds and 64ths.
Do you absolutely need something this fine for woodworking itself? No, not really, a decent wooden try square and dividers or a compass could substitute. After 40+ years the decent one I got for Christmas as a kid was pretty well shot--my father was a journeyman tool a die maker in the '50s and '60s so it made sense to him to get me a decent one. I had the money so I got the Starrett maybe 10-12 years ago. The old one resides in my carpentry tool box as it still has utility for carpentry when used with a pencil. The Starrett resides in my shop's precision tool drawer with calibers, dial gauges, etc. and is used for metal and woodworking and tool set ups.
P.S., It doesn't hurt to treat yourself occasionally. Back in the '80s I did a 3.5 month solo bicycle trip all over the east coast. While in FL I met a lot of middle aged and older people who were curious about my loaded down bicycle and what I was doing. I heard a lot of stories that started out with "I always wanted to..." None of those desires were carried out by the story tellers and there was disappointment in a lot of voices. It gave me a different perspective on life than I would have had otherwise. You need to take care of yourself.