I am vegetarian and have been to both. They both have good vegetarian options. In fact, it's short-changing Boma to say there are just "options". I felt like I could eat half or more of what was offered at Boma - and the offerings are extensive.
While there are unique vegetarian items on the menu at Jiko, and it receives RAVE reviews, I have been disappointed with my entrees both times I have dined there. The first time I had the peas and grains dish. It was fine, but not the tastiest thing I've ever eaten. I would characterize it as a big, colorful portion of kind of blah stuff. The last time I ate there I had the stuffed piquillo peppers. This came with beans that were "al dente" to say the least. It was not a generous portion at all, and for me, the beans were very unappetizing. I understand al dente pasta, and risotto not cooked to mush, but al dente beans? I like my beans cooked through. The appetizers at Jiko are mostly outstanding, though. I've just never had an entree there that I would order again.
Now, Boma is a different story. The soups there are outstanding. I liked the squash soup and the mushroom soup. The sides and salads are varied and fresh. I really liked the pasta salad (really different!), the falafel, and one of the squash dishes. I liked a lot of other stuff too -- there's just so much, I can't remember it all! The menu posted on allears is really just a fraction of what they offer. P.S. The desserts are delicious, too.
Long story short (too late), my suggestion would be Boma. It's certainly the less expensive choice! The only con is that the buffet experience is less than satisfying sometimes. You feel like you tasted a lot, but didn't eat much of anything. Even so, we're planning on doing Boma on our next trip, but Jiko didn't make the cut.