The main disavantage of the synchronous mode is that in order to overclock your memory, you will need to overclock your CPU. Usually that's ok since maybe you are trying to overclock both memory and CPU. But in many cases the maximum external clock your CPU is reaching is limited by the memory or vice-versa.
For example, by trial-and-error basis you found out that the maximum external CPU clock you can configure on your system is 180 MHz. So, your memory is also working at 180 MHz ("360 MHz" since DDR memories are rated with two times its real clock) or more, depending on the host/memory ratio settings that some synchronous motherboards have. For example, on the motherboard of Figure 4 the memory can be set to run with the external CPU clock multiplied by 2 or by 2.5. This motherboard was targeted to Pentium 4 CPU, so when the external clock was set to 133 MHz ("533 MHz"), the memory clock could be configured at 266 MHz or 333 MHz. Of course setting it to 333 MHz would make more sense if you use DDR333 or DDR400 memories. But when we overclocked the CPU external clock to 180 MHz, at the 2.5 ratio shown the memory would run at 450 MHz.

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Figure 4: Host/memory ratio setting.
So, on motherboards with synchronous mode, when you find out the maximum CPU external clock you cannot know for sure what is limiting you to increase the CPU external clock. Can be a CPU limitation or can be a memory limitation. On motherboards with the host/memory ratio configuration shown on Figure 4 you can change the ratio to check which component is limiting the overclock. For example, we would lower the ratio from 2.5 to 2 in order to make the memory tun at 360 MHz instead of 450 MHz and then try again to increase the CPU external clock. If you really cannot increase it over the 180 MHz limit (in our example), it means that the CPU is the component limiting the clock increase. On the other hand, if after lowering the ratio you now can increase the CPU external clock a little more, it was the memory that was limiting the overclock. Then you can see the new maximum external CPU clock you can achieve with this new configuration.
When the CPU is limiting the clock increase, your have to face a terrible truth: your memory could achieve a higher clock rate, but you cannot configure it to use this higher clock rate because your motherboard doesn’t have a configuration to do so. That's one disavantage of using cheap motherboards and that's why overclockers perfer high-end motherboards.
So, this problem doesn't affect motherboards with asyncrhonous memory configuration. Since you have two different configuration sets for CPU and memory, the maximum clock the CPU can reach is not limited by the memory, and also the maximum clock the memory can reach is not limited by the CPU, which is far better for overclocking.