Sveaborg was bombarded by ten liner's and nine frigates for two days, and overall effect was limited. Forts and batteries weren't silenced and their fighting power wasn't significantly reduced. Russian total losses were 73 killed and around 300 wounded.
If you'll excuse me, I'll quote from contemporary descriptions of the "limited effect".
...after a little spell, batteries from all directions on shore sent shot and shell out in return, but so many fell short that it was soon reduced to a few guns of long range, and two or three uncomfortably heavy long-range mortars, which sent shot and shell well out to the line if they wished to. But soon our gun-boats went in and began firing at shorter ranges, and this made the fire from the shore little or nothing for the mortar-vessels, and they steadily went on, causing little clouds and occasionally more smoke, which soon began to show itself in good columns of smoke, and fires were established in several places.
About ten we could see we were evidently successful, and that total destruction was only a question of time. At ten a magazine blew up, bringing rounds of cheers from the crews of the large ships swarming on every top and yard like bees. Still went on smoke and fire, followed by flames through roofs and windows. We were running up and down along the line, with the admiral on board, occasionally being able to swear we were under fire by a stray shot dropping near us, and one shell of the big mortar (named 'Whistling Dick', after his Sevastopol brother) bursting a little over us, throwing the fragments on both sides of us, but not one touched us anywhere. One of my greatest pleasures, next to the feeling that I had proved to be right in my ideas about the effect of shelling in this way, was to see the changed visage of the admiral: instead of the anxious, thoughtful face of past weeks - anxious to do all he could, doubtful if any success to warrant the risk could be gained - he was looking bright and cheerful, and expressing surprise at the result. At twelve another small magazine exploded, bringing more cheers; but at 12.15 a tremendous column of smoke, mixed with fragments of all kinds, masses of timber, etc., showed we had found out a large one; but no sooner was the astonishment over and the cheers roaring in different directions, than up went another column and more fragments, and again another and another, with only intervals of seconds, till at least twenty explosions had followed the first in quick succession. Occasionally towards the end a longer interval would make us think it was over, when again masses of building would fly up in all directions, but all near one spot. At last it reached a larger new earthen battery on the top of Gustaff Island, and away went one side of it, guns and all, leaving, instead of bright-green turf, a heap of stones and rubbish. I think it was all on the inner slope of Gustaff, where I have written m. Now nothing is to be seen about there but bare space; and even on the next island, Vargon, the buildings on the point nearest to it are a heap of ruins. I think such an extraordinary explosion never occurred before. There might have been greater single ones. The fort I was under at Bomarsund, from the account of those who saw both, was a more tremendous explosion than the first; but a succession of at least twenty - some say thirty - is the extraordinary part. I think they must have had the magazine formed in cells or compartments of masonry, and that these went in succession, each blowing up its next-door neighbour by smashing the intervening wall, which might have caused the second or two's interval between each.
(some days later)
While clearing, at noon I got a gun-boat from the admiral, and went to the east side of the place as far as I could to look through the islands. The arsenal fire was still raging, and the ruin over the back part of Swarto, as well as Vargon, was complete. The devastation caused by the grand explosion was terrible on Gustafsvard, but my friend the white house had only one shell-mark, and a house beyond it was uninjured; the long house west of it was burnt out at its south end, showing the extreme limit of destruction in that part. In the evening I went in my boat with Creyke to a nice place for looking between the islands from the westward, an island off Helsingfors, with a high rock, but only two thousand yards from all the Helsingfors batteries. On all the batteries men sat quietly looking at us, officers watching us with spy-glasses, but they did not fire. From there we saw that within the limits I have shown dark the destruction is so complete that not even a portion of a house is left, all a blackened, shattered ruin, but the windmill and two wooden houses on the eastern front, which seem to have been charmed. Between the large black building on the west end of Swarto and the church just outside our range, a little cluster of wooden houses stands quite uninjured, affording a striking contrast to the blackened ruins. The space between that black building and the long storehouses in the middle of Swarto is covered with the ruin of smaller stone houses, apparently dwellings.
The bombardment of Sveaborg did considerable destruction to the targets. Within four hours of opening fire, magazines on both Vagen and Gustavsvard have blown up; fire eventually consumes all the dockyard buildings, workshops and stores on East Svarto, with lesser damage being done elsewhere.
It's true a lot of this was done by mortars instead of direct fire, but then the fortifications at Sveaborg were quite modern and there was a significant Russian fleet present (four ships of the line, etc). It does nobody any good to pretend the above was little damage - Sveaborg was very badly damaged.
They also weren't going after the batteries themselves - they were going after the important materials, and fulfilled their objectives.
Of course, this was all done with smoothbores. We know from engagements of the Civil War that second- and third-system forts were quite vulnerable to rifle fire such as Armstrongs, and that at the range British liners dropped anchor to bombard forts in the Crimea (800 yards or so) they could score hits quite nicely and could collapse the facings when their shells burst inside. The US bombardment mounted at Fort Fisher sufficed to silence it within an hour or so, and the British could easily manage that kind of attack with the forces present on NA&WI station (though they probably wouldn't need to, Fort Fisher was an earthwork fort which was much more resilient to large shells than the masonry of Forts Monroe, the New York forts etc.)