There's two ways to tackle this question. First being how effective were the Tigers were on a tactical level, as in how effective was it at breaking Allied positions/destroying Allied armor/defending a position that is under attack. The second is how effective was it at the strategic level, as in how did Tigers contribute in the grand scale of Germany's war effort as a whole. Lets tackle both respectively.

The Tiger I was designed initially as an offensive breakthrough tank. Namely, to advance and punch holes in the enemy's frontline for exploitation by faster armored vehicles and infantry to rush through. With the Tiger I's final design including frontal armor of 100 mm and armed with the 88mm KwK 36 gun, the Tiger I's proved to be a formidable opponent, able to destroy Allied armor at ranges up to 4000 meters, and no allied guns available at the time could reliably penetrate a Tiger's armor from ranges outside of the Tiger's own effective range.

In actual practice on the battlefield though, the Tiger I rarely served its intended purpose as an offensive breakthrough vehicle, but instead was fielded in defensive roles almost exclusively as Germany's ability to conduct offensive operations was neutered by the time the Tiger I entered service in large numbers. From responding to breakthroughs made by the Soviets to counterattacking to retake lost positions on the frontline. While the Tiger I was effective in this role, the low numbers of Tigers available compromised Germany's ability to use them as a reliable method of blunting Soviet breakthroughs and counterattacks.

The appearance of the Tiger I on the battlefield in the Autumn of 1942 also prompted the Allies to respond to the new threat in kind. When the Tiger first appeared on the frontline near Leningrad, a Tiger became stuck in the swampy ground and was abandoned, giving the Soviets one perfectly intact Tiger tank to study and prepare countermeasures for. The Soviets responded by restarting production of the 57mm ZiS-2 cannon, along with development and up-gunning of their tanks to equip of 85mm D-5T cannon, along with production of new armored vehicles that would eventually settle on the IS-2, equipped with a 122mm cannon that proved more than effective against the Tiger's armor.

The Americans and British also responded to new advances in German armor by upgrading their guns and armor as well. The British began developing armor that could incorporate their 17-pounder anti-tank gun. With a converted Sherman tank built to hold the 17 pounder becoming the Sherman Firefly, the introduction of the Comet tank in 1944, and increased production of the 25-pounder towed anti-tank gun, the British were well out-fitted to handle the Tiger and the newer Panther, introduced during the Battle of Kursk in 1943.

The Americans also upgraded their Sherman tanks to hold the longer 76mm cannon with increased penetration to handle Tigers, as well as development of the M26 Pershing armed with a 90mm gun, designed as a counter to German heavy tanks. The Pershing would not see service until the final months of the war, and upgraded Shermans such as the Easy 8 were not fielded in incredibly large numbers, citing the low numbers of Tigers encountered as a reason for not fielding more.

With these new allied guns blunting the Tiger's tactical advantage further and further, Germany began development and production of the Tiger II in order to keep pace and counter these new Allied vehicles. The Tiger II incorporated the Panther's sloped armor but with its thickness increased from the Panther's 85mm to 150mm at a 40' slope. The Tiger II also included the 88mm KwK 43 L/71, an upgraded version of the Tiger I's main gun, capable of destroying nearly all Allied vehicles available in 1944.

The Tiger II looks like an absolute monster on paper, but the state of the war in 1944 when it was introduced meant that it would almost never be in a position where it could serve its purpose as a breakthrough tank for offensive operations, and Germany's reduced industrial capacity due to bombing and other wartime production demands meant that less than 500 Tiger II would ever be produced, nowhere near enough to actually be used in large enough numbers to matter on the battlefield. What's worse is that the Tiger II suffered from an underpowered engine, wholly inadequate parts to handle its extreme weight of over 70 tons, and weaker quality steel for its armor, leaving the upper hull of its armor weak to the spalling effect of high explosive shells. Tactically, the Tiger II was a failure due to its own mechanical and production shortcomings. It was almost never able to be at the battlefield where it was needed because of low production numbers and mechanical breakdowns caused by its own weight.

Now we take a look at the bigger picture of the Tiger I and II, their strategic value in the grand scheme of the war. Factors such as cost, numbers produced and production process, and overall impact on the war.

Both Tigers were incredibly expensive and labor intensive to produce. with the Tiger I costing around 4 times as much as a StuG III assault gun, and Tiger II costing over 3 times as much as a Tiger I to produce at 800,000 Reichmarks compared to the Tiger I's 250,000.

The amount of man hours, money, and time spent into making these tanks in the small numbers that were produced, with just over 1,300 Tiger I's and less than 500 Tiger II's actually made, these tanks are largely seen as not worth the immense effort poured into their production; factoring in the lesser monetary cost, production cost, and labor hours that could be made to produce more numerous Panzer IV or StuG III's to have more armor available across all fronts, even if that armor is not as effective as a Tiger's.

There is also another linchpin to take into account, and that was Germany's resource availability. Simply put, Germany was never going to be able to produce armor at the numbers necessary to keep parity with the Soviet Union and the United States. While Germany could produce 8,000 Panzer IV's, it was never going to keep pace with the nearly 50,000 Shermans and 35,000 T-34 tanks produced. It can be argued that the Tiger tanks were produced taking Germany's resource shortages into account. If Germany simply cannot keep parity with their enemies in terms of raw numbers, then Germany's vehicles had to become so overwhelmingly superior to their enemies that one Tiger could do the work of 10 Panzer IV's and be worth the opportunity cost of just making more Panzer IV's.

At the end of the day, Germany's Tigers were indeed fearsome machines that earned a reputation for their deadly performance on the battlefield, but it was not enough to win them the war. With such few numbers actually produced, and the large sink of time and effort to even produce them, Germany simply could not make enough Tigers to keep control of their frontlines, as they weren't available in meaningful enough numbers to actually have a decisive impact on Germany's war effort.

Edit: the slope is 40', not 45'.