The first thing to remember about the comparison of the Barracuda & the Avenger is that although they served at the same time in WW2, they were a generation apart in development timescales at a time when, in the late 1930s, aircraft were developing at a rapid rate..
Barracuda development began in early 1938, with the contract for the prototypes issued in Jan 1939. By mid 1939 the RN expected production to run between April 1941 and April 1942, implying that there would have been a new design intended to come along to succeed it in service design of which should probably have begun about 1940 (the RN did issue a Spec E.28/40 in Feb 1941 for a research aircraft "for full scale investigation of the problems associated with increased weight of deck landing aircraft" which had all the characteristics of a new TBR design). Then came a host of delays with the result that production didn't start until April 1942 with squadron service from Jan 1943. And we then have to take account of the internal problems at Fairey under wartime conditions which frustrated the Admiralty and MAP.
Grumman received the contract for the prototype XTBF-1 on 8 April 1940 by which time there was a much greater urgency to progress its development, WW2 having started and the USN planning a major expension of its naval aviation arm and with the TBD Devastator long out of production. So its development was accelerated with production starting in Jan 1942 and the first aircraft seeing combat at Midway in June. But even its initial development did not prove trouble free. It just seems that greater urgency in a peacetime environment during 1941 allowed them to be sorted more quickly. And the Avenger did not meet the speed requirement that was initially sought by the USN (300mph).
Two years in the late 1930s meant a huge amount when aircraft development was racing ahead.
It also needs to be noted that the initial requirements called for in the Barracuda were fairly tightly drawn in terms of aircraft weight (10,500lb), free take off distances (British carriers generally had shorter flight decks than those of the USN) and speeds (76mph as generated by the catapults of the time in zero wind) and landing speeds (stalling speed 67mph). As I've noted in other threads that had an effect on the design of the Barracuda and its competitors. These limitations were set in part by the capabilities of carrier catapult and arrester gear of the period. Operationally Barracuda II/III in WW2 were flying at weights up to 14,250lb. And that without any increase in wing area. The RN only began to relax its landing and take off limitations in 1940 while at the same time beginning to uprate their shipboard equipment.
But there was also a significant difference in wing area of the two types that would have further increased the Barracuda's wing loading. Avenger 490 sq ft. Barracuda 405 sq ft. The Avenger also had about 5ft greater span. The Fairey Youngman flaps fitted to the Barracuda were supposed to have the effect of adding to the wing area during normal flight so increasing its efficiency. But it seems to me that with shorter wings of less area and the requirement for a low stall speed the Barracuda wing must have been significantly thicker than that of the Avenger, which wouldn't help its drag despite the benefits of the flaps.
The USN did not set such restrictive limits in the first place although its flight deck equipment was not significantly more advanced that that of the RN. It is worth noting in this context that the Curtiss SB2C Helldiver ordered in May 1939 also suffered huge weight growth during its gestation period and also suffered great delays. Designed for a max weight of 10,189lb it entered service in SB2C-1 form with a max weight of 16,607lb, over 3,000lb of which increase came from the airframe.
The speeds more usually quoted for the various versions of the Barracuda are:-
Mk.I - Merlin 30 - 235mph at 11,000ft; economical cruising 138mph at 6,000ft
Mk.II - Merlin 32 - 228 mpph at 1,750ft; economical cruising 172mph at 5,000ft
Mk.III - Merlin 32 - 239mph1,750ft; economical cruising 170mph at 5,000ft
There were a number of features on the aircraft that would not have helped its drag. The whole folding mechanism was very efficient in reducing the folded width and the space it would take up on a carrier deck, but there were a lot of joints and edges and protruberences that could not have been sealed entirely and would undoutedly have added to the drag. Things like the brackets on the upper surface of the wings that locked into the tailplane when the wings were folded. Also the V shaped handling rails that folded into the underside of the wing to assist in the manual wing folding (this a product of the high wing, itself a product of the emphasis given in the design to the view from the observer's cabin). The various bits and pieces can be seen in this photo of the wing folding in progress.
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The Avenger of course used Grumman's Sto-wing that was equally as efficient at reducing the aircraft folded width and had the advantage that it was powered, but did not have so many joints causing airframe imperfections.
And carrying its entire weapon load externally which required bomb carriers to be attached to the wings as a dive bomber, as in the preceding Swordfish & Albacore, was not so efficient. But with the requirement to carry no bomb larger than 500lb at the time of its design perhaps understandable. The bomb racks are visible in this photo.
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Bombing up a Barracuda. Note all the panels and holes in the wing. How well could they be sealed?
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The Barracuda's problems go much deeper than simply being underpowered. No better example is what happened when Fairey began to look at developing it further from June 1943 into what eventually became the Mk.V. Simply adding a single stage supercharged Griffon to a Mk.II airframe did not solve the Barracuda's problems (1,890hp Griffon VIII or 2,020hp Griffon 37 was eventually used in the Mk.V) . So began a series of other "improvements". It was put on a diet (despite the heavier engine weight growth of the airframe was limited to 1,300lb in the final version), the airframe was cleaned up by filling and fairing aerodynamic imperfections, the ASV.II radar aerials replaced with the pod of ASH radar, a modified tail fitted to improve dive qualities, a tail fillet was added to improve directional stability, an enlarged wing with square wingtips increased the wingspan by nearly 4 ft to reduce wing loading, new enlarged ailerons to increase maneuverability and last of all a pointed rudder. Despite all the changes the speed only increased by about 20mph!
In mid-1945, the Barracuda squadrons in 11ACS heading for the Pacific undertook a number of changes to their aircraft to reduce weight and improve aerodynamics. The TAG was deleted from the aircrew along with his guns and ammunition, the ASV.II set and its Yagi aerials was removed, and the bulged observers windows replaced with flush fitting perspex. I've not seen any figures for the effect that these changes had on the performance.