I tried to use the cannon a couple of times. No dice.
Short range, high TUs, inaccurate.
I gave it to my best heavy weapon soldier, supported by a sniper and SMG, all in nano-armor. Used it in an indoor fight, one large room with two entrances leading to a smaller room with stairs, everything was short range. Opposition was three Tamans in medium armor, armed with two plasma rifles and a plasma blaster. I was running this on standard difficulty.
I tried multiple save game reloads and methods of using the cannon. It never out performed the sniper rifle, indoors, at close range. The SMG is rather overpowered under current circumstances, but the alien armor difference is quite noticeable and I expect it to stop being useful with stronger aliens and heavy alien armor.
On reaction fire the SMG gets about two to three sprays per sniper shot, the sniper was getting two to three reaction shots per cannon reaction.That was trying the RF fire camping of the doorway to the other room. The cannon suffered from not just slow reaction, but it missed more than the other weapons too.
In an assault role it suffered from the high TUs and higher miss rate, damage seemed comparable to sniper aimed shots. Biggest issue here was getting people across the large room without dying from multiple plasma hits, the high TU cannon and both rifle suffered here but the SMG couldn't reliably kill aliens fast enough either. I regretted not bringing a flamer for this.
Playing peek-a-boo (breaking LoS to the doorway to lure an alien out then coming out to fire and hiding again) the cannon would have been as effective as the sniper rifle if it had been as accurate. The SMG and headshots from the rifle won out in this tactic, but a couple of plasma 'nades and GLs would worked better.
I've just used the particle cannons as income since then. Had similar experiences with the plasma blaster. While I do agree with BT about the beam rocket thing (although the response was slightly tactless, he has answered that before) there will need to be some advanced human weapon systems to take over the roles of the sniper rifle and close combat weapons without relying on the aliens for your ammunition. More and more in late (current) game missions I'm starting to lean toward heavy laser and GL squads with a 5/3 split. No alien can survive 4+ laser hits with GL support firing around corners and through windows/doors.
A sniper version of the bolter rifle? Plasma and gas rockets for the rocket launcher?