The trouble with discrete parts is that they come with parasitics; e.g. an inductor will have a parasitic resistance, parasitic capacitance, and parasitic capacitance to the board. Generally speaking, as you approach 1GHz, parasitics start affecting your frequency response, even on small SMD components. Even if you buy "10 GHz" components, they'll have parasitics. The hard part of RF design is modeling the parasitics accurately (and knowing where they can be ignored). Also, there's a trade-off between precision and cost.
Microstrip elements are more abstract, so you generally have more control over what's going on. As others have mentioned, though, they are bigger.
Modeling components is time-consuming. Keep in mind, though, for a one-off project, you might find that tweaking the circuit is enough to get it to work. Repeatability over hundreds or thousands of units is a different matter. For this spectrum analyzer project, you don't need to worry about the 10.7 MHz IF blocks, but you will have to be careful with the 1-2GHz stuff. The bandpass filter looks like the most difficult part.