One big question you need to have answered prior to getting a good answer on what antenna you should use is this. "Is the system you're trying to monitor a simulcast system of not?" With a simulcast system, they broadcast using several tower sites on the same frequencies as a way to better provide handheld coverage in the area. The typical scanner has quite a bit of difficulty decoding a simulcast system if it picks up more than just a single tower site. You are often better off with a lower gain antenna than a higher gain antenna since your chance of picking up more than a single tower increases with your antenna gain.
Often it's better to use a very directional antenna pointed at a single tower (and no other on the system in the direction that antenna is pointed) than a high gain omnidirectional antenna. Now most likely that highly directional antenna will have quite a bit of gain, but that's OK since the directional pattern will only pick up the single tower site you have it pointed at. Be aware that depending on the system and tower site pattern you may actually need to point at a more distant site than the closest one if your closest one has another site along the same (or nearly the same) path.
To help answer your specific question, you most likely do NOT want the discone since it has a very wide frequency range coverage so you're wasting most of your antenna and its performance where you won't be listening. Also, most discones are rather poor at the 700+ MHZ range. Instead of designing it for that range, they chose to make it work from the VHF-Low, VHF-Hi, and UHF (below 500 MHZ) ranges and basically just hope that it will pick up the higher frequencies.
Including a link to the system or systems you're wanting to monitor will help us best answer your question.