Forbidden City vs. Summer Palace
The Forbidden City was the Emperor's "office" and formal residence, while the Summer Palace was his vacation home. The Forbidden City is all about rigid symmetry and power; the Summer Palace is about fluid landscapes and beauty. Recommendation: Visit both if possible, but the Forbidden City is the primary historical heart of China.
Forbidden City vs. Temple of Heaven
The Temple of Heaven is a park where emperors performed annual sacrifices. It's much smaller and easier to navigate than the Forbidden City. Recommendation: If you only have half a day and want a relaxed stroll, Temple of Heaven is better. If you want the core imperial experience, Forbidden City is mandatory.
Forbidden City vs. Ming Tombs
The Forbidden City is where they lived; the Ming Tombs are where they were buried. The Tombs are located outside the city and are much more desolate. Recommendation: The Forbidden City is significantly more visually impressive and historically dense.