The Tiger was mostly a problem for Allied tanks because it was 2-3 times as heavy as most of them. However, even when the Tiger just hit the battlefield, the Allies already had weapons that could defeat them. The first ever Tiger to be knocked out was destroyed by a humble 6-pdr gun from a fairly long range. Bigger guns like the 76-85 mm AA guns could even knock it out from the front, not to mention bigger pieces like 105 mm or 122 mm artillery. Those guns were put into tanks in fairly short order.

Mostly, the Tiger's reputation is based on rumour. For example, the 82nd Airborne, or indeed almost any American unit, would not have ever seen a Tiger, since the Americans only saw Tigers three times. Watch that video, by the way, it's pretty great.

If you want to read about the Tiger's overall mediocrity in great depth, click here

Far be it for me to say anything that might slight your grandfather's service, but as /u/TankArchives notes, if he served in Normandy, it is extremely unlikely that he would have seen a Tiger. There were a hundred and fifty Tiger tanks in Normandy; all of them were deployed around Caen against the British, since the Germans considered them superior opponents (they later admitted to have underestimated the Americans). Stories about Tigers in the bocage are often the result of American tankers spotting the very similar turret of the far more common Panzer IV and panicking. In fact the Sherman was more than capable of taking the Panzer IV on even terms.

Sources:

Antony Beevor, D-Day: The Battle for Normandy

Nothing, Panthers are very overrated, they were produced to destroy enemy tanks, they were good at it, but thats all, they had very bad transmission and Panther's canon have bad HE power, which Made it usseles for infantry support, which Made infantry vulnerable to enemy fire.