There were more police/guards than tourists when I was there at Easter (and, there were a lot of tourists)...
Please note Tikal is not Disney-fied. When you climb to the top of Temple 4, you are on a thin ledge surrounding the highest Mayan ruin in the world...no fence...just a guy with a stretcher at the bottom! Wear proper shoes. Don't mean to patronize, but I met a injured people who were wearing sandals/flip flops.
All the warnings posted on Lonely Planet and the other backpacker type sites stated that most problems were experienced by people in vans or buses that were pulled over in so-called road blocks. Katie at Maya Travel arranged flights and private driver for me, and it was fine. We did pass one road block on the way from the airport to the Jungle Lodge, but they waved us through.