I've done about 4000miles and 6 track days on my KTM 660 so far and used a small selection of tyres available but this guide may help if your unsure what to try next.
Pirelli Scorpion Sync
Good all round tyre, ideal for first time supermoto rider and standard fit on many new models including the KTM LC4 range. This tyre has a good operating range temperature wise and offers good feedback in all conditions both on track and road. This tyre is however out of its depth with those who like big lean angles with foot out action as they soon overheat and lose grip, ditto high speed corners.
Metzeler Sportec M1 rear + Metzeler MEZ3 front Z rated
Many will advise against the use of Z rated tyres as they need a bit of warming up especially on the front as supermoto's are so light. This pairing isn't recommended for winter use but was a big improvement over the scorpions during summer on warm tarmac. Pressure was dropped to 26psi front to aid heating, feel when on the brakes into corners on the track was excellent as was feedback from the rear while hard on the gas. Both tyres also performed well in the wet as well.
Maxxis Intermediate Hard / Road compound
Recommended by many in the supermoto fraternity as the ultimate road and track day compromise. Don't believe the hype! Although the tyres have good cold grip (in a staright line) they don't improve much with heat. Any more than slight dampness causes them to run stone cold (even with ridiculously low pressures) leaving the throttle almost useless out of turns. Feel both on the brakes and on the gas is about as good as your grandads 3 pack of Geronimo's, and any extra grip that you may or may not have over any other tyre is about as reliable as a party political broadcast. Consistency is the biggest problem, especially on the rear on the road. You can literally do a set of bends and be impressed with the grip, turn around, ride through them again and find yourself all over the show, which leads to your confidence getting shot.
I never used the front on a fast track but the rear overheated and chewed up quickley on a sunny Donnington park, which caused the back to light up uncontrollably out of sharp turns on the melbourn loop. Needless to say it was quickley changed.
On the plus side you'll never wear the front out and in a straight where you can trust the rear you can pull mega wheelies even in the wet. They also performed very well on the dirt section of the supermoto track. If you must try these tyres make sure you go for the medium or soft compounds as these should be an improvement. I personaly won't be risking any more hard earned cash on shonky tyres made by a company that probably see's Cheng Shing and Woosung as it's main rivals.
Dunlop Intermediate Race tyre front (not supermoto only)
While at Donnington and also on the road over winter I had a Dunlop Intermediate race tyre on the front with the rear Maxxis. It always gave confidence and enough grip on the road whatever the weather, but failed to impress at Donnington on a dry sunny day. The front would often tuck going flat out through the craner curves mainly when you have to flick the bike over hard from right to left. The tyre never seemed to warm up enough to give consistent grip at speed although it was fine on slower corners and under braking. I used it on a soaking wet Chippenham supermoto track in November and had no problems although the speeds never get high there and the front is constantly loaded.
Michelin Pilot Race (hard compuound) Rear + Michelin Supermoto Cut Slick Front
I've only used these tyres at Donnington Park in the dry on a warm day. The front was spot on around the whole track at all speed although I did use tyre warmers so they weren't ever too cold. The front slick held it's heat for a while after a stop and suited the KTM's handling brilliantly. The rear wasn't as good, this is a sports bike tyre and the KTM never seemed to be able to heat the sides of the tyre enough to get good grip although it was a big improvement over the overheating Maxxis. Despite the lack of grip again flicking over flat out (110 - 115mph) on the Craner curves and losing drive around the melbourn loop it did have plenty of feel like the front. So any spinning or movement didn't cause loss of confidence, on a sportsbike once warm these are the nearest road legal tyre I've used that compares to a proper slick race tyre. Unfortunatly the KTM just doesn't have the weight to warm it up properly, the medium or soft compound versions would probably be quite good.