There are a few key differences between each route. One way or another you're going to miss out on some stuff.
For both routes, you will receive an item as a prize. For the Joja route, you'll receive a soda machine, which gives you one free Joja Cola each day. For the Community Center (CC) you get the Stardew Hero Trophy, an exclusive furniture item.
If you finish the CC, Pierre's shop stays open every day of the week (doesn't close on Wednesdays). There's no equivalent prize for Joja.
As Wrigglenite explained, each CC bundle will reward you with items once complete. Most of the time these items are pretty "meh" but some like the Crystalarium can be very helpful if you manage to get them early.
In general, the Joja route is typically much easier and faster to complete, but the CC gives "better" rewards. In my playthroughs, I've been able to complete the Joja route by Fall of year 1, but the CC can't be completed until Summer year 2 at the earliest (unless you get really lucky with the Traveling Cart).