Some good answers here, but I will try to give you my ideas.
The Panther had a better gun. Although the 88mm of the Tiger was heavier, it could not penetrate as much armour as the 75mm. The Tigers 88mm L56 was a re-mounting of the FLAK 36 AA gun. However, the 75mm L71 of the Panther was a purpose designed AT gun. The longer barrel length offered greater payback as far as velocity and accuracy was concerned. As a rough guide, the 75 could penetrate about 150mm of vertical armour. The 88 could penetrate 120mm (The same as the 75 L48 used by the PzrKwgn IV. However, the weight of shell meant that it could achieve this penetration at a longer range that the Pzr IV).
The Panthers original spec was for 30mm of frontal armour. However, by the time that it reached production, this had increased to 50mm. This lead to a few mechanical problems. While the Mayback HL230 P40 was capable of moving the added weight, the gearbox wasn't. Concequently, when first deployed during the Kursk offensive in 1943, the Panther suffered from several breakdowns as the gearboxes struggled with the extra weight. Another consequence of this was that the wheels, which were designed to support a lighter tank, were prone to cracking.
When viewed from above, the Tiger is a squarer tank than the Panther. This presents difficulties for the Tiger, since it means that, in order to be loaded onto railroad cars, the outer set of roadwheel must be removed and thinner tracks fitted. The Panther, on the other hand, was designed to be thinner and could therefore be moved to where it was needed quickly. One advantage of this for the Tiger however was that the wider front aspect meant that the chance of offering a flank shot was less compared to the longer body of the Panther.
The weight of the Tiger made it slow. It could not react quickly to changes, since it took a great deal of effort to move the turret around. The tiger had an auto traveres peddle, but even so, the weight of the turret, made from 80mm thick steel, would take a lot of effort from the engine.
A report detailing a Tiger captured in Tunisia by the British showed that, although the Tiger could be penetrated from the rear, at various ranges by different calibre weopons, at no time could a British gun penetrate the front or side of the vehicle, even using 17lb rounds.
The introduction of APDS rounds helped to overcome this. However, this report had helped to shape British military doctarin regarding this vehicle, especially after the mauling given to allied vehicles in Italy. One such occasion saw 24 allied tanks (Shermans I believe) facing four Tigers at long range. Within minutes of the Germans opening up on these vehicles, 12 were knocked out. The crews, faced with four dug in tigers did the only sensible thing in open country, they abandoned their tanks and ran.
In Normandy, the allies applied a ratio of 5 Shermans or Cromwells to take out one Tiger. The idea was that the Tiger would knock out 4 allied tanks, giving the 5th the chance to get behind the Tiger and knock it out. The same ratio was applied to the Panther. However, the Panther was lighter and faster. It could reposition a lot quicker than the Tiger.
While Germans tended to overengineer their vehicles, this was especially true of the Tiger. It was said that you could steer the vehicle with two fingers, due to the precision used to machine the geering. This meant that it was more expensive to produce than the Panther.
The shape of the Mantlet on the Tiger was straight up, hoizontal. This actually worked for the Tiger. The rounted mantlet of the Panther offered a fire trap. Although, if a shell hit the top of the mantlet, the round would bouce upwards, if it hit the bottom of the mantlet, the shell would be deflected downwards, onto the weaker top of the vehicle. It was only in later models of the G that the lower part of the mantlet was squared off.
So, overall the Tiger was a great tank. However, its expense made it less atractive than the Panther. The Panther suffered from several weaknesses early on, but these were pretty much sorted out by the late G period. Both were excelent vehicles, but I would have to say that, due to expense and serviceability, the Panther actually wins. This is, I believe, shared by the Germans themselves. Just look at the Konigstiger and tell me which vehicle it looks like, the Panther or the Tiger.
Luck