Ok. I just got the Blackguard Hood(and Armor) So I tested this. Unfortunately, the Masque of Clavicus Vile is stored somewhere safe(don't remember where). I do have Volsung, though and can simulate the effect by activating a Shrine of Dibella. FYI my character is a breton female level 151 and has 100 speech with Haggling 5/5 and all perks on the left(which I will be making legendary for a portion of the test).
Normally just Volsung and my 35% barter necklace get me the best prices with all merchants male and female except Enthir and the Dremora Merchant(full inventory value on an item when selling, full inventory value +5% when buying). First I spent the night at the inn in Dawnstar, then started talking to blacksmiths Thoring(Nord male) and his wife Seren(Redguard female). I checked the selling price of a Flawless Diamond without gear, with the Hood, with the Mask, activated the Shrine south of town and used the mask again, made the skill legendary and tried again.
At this point I couldn't sell the Flawless Diamond anymore because blacksmiths don't buy them without the merchant perk. I switched to a Gold Ingot due to having a nice even value(100) like the Flawless Diamond(1000). I then reloaded and made the skill legendary without the shrine blessing and tested with the no gear equipped and just the hood equipped. This should pretty much cover all conditions except for a character with Speech between 90 and 100. Results:
Flawless Diamond with 100 skill, all perks and no gear-Thoring:904 Seren:747
Flawless Diamond with 100 skill, all perks and Hood-Thoring:N/A Seren:910
Flawless Diamond with 100 skill, all perks and Mask-Thoring:N/A Seren:877
Flawless Diamond with 110 skill, all perks and Mask-ThoringN/A Seren:877
Brief pause. This proves skill over 100 has no bearing on prices. I also excluded Thoring from the last 3 tests because the price with him would have been maxed out using the gear and would not have given an accurate picture of exactly how these particular items were affecting the prices. Now on to the test results after making Speech legendary(15 skill base and no perks):
Gold Ingot with 25 skill, no perks and Mask-Thoring:50 Seren:45
Gold Ingot with 15 skill, no perks and no gear-Thoring:41 Seren:37
Gold Ingot with 15 skill, no perks and Hood-Thoring:50 Seren:45
I think we can reach a few more conclusions after looking at all the data as a whole. At 100 skill(natural, not buffed) The Blackguard Hood gives better prices than the Masque of Clavicus Vile due to the Hood having a better straight up Barter percentage and the Speech enchant on the Masque having no effect. At 15 skill the Masque and the Hood seem to be having the same affect on prices. This should remain the case up through level 90 (including actual skill and other temporary speech buffs like the blessing, Gift of Charity and Glibness mixtures) but the Hood will pull ahead of the Masque between 90 and 100 as the Speech effect on the Masque diminishes.
I think we can also determine that if you had to choose between say an Amulet of Zenithar(10% better prices) and an Amulet of Dibella(+15 Speech) or the Shrine of Zenithar(10% better prices) and the Shrine of Dibella(+10 Speech) that Zenithar is better as far as bartering goes. At minimal speech skill the Blackguard Hood(25% better prices) is giving the same effect as the Masque of Clavicus Vile(20% better prices and +10 Speech) which indicates an extra 10 speech is only worth 5% better prices.
Another conclusion we can draw(unrelated) is that the effects of the Allure perk carry over after making the skill Legendary. I had read in the bugs section of uesp's page on Speech that vendors still have an extra 1000 gold and one still retains the ability to invest with merchants after making Speech legendary despite not having those perks anymore. I guess I shouldn't be surprised, so we can add Allure to the list of perk effects retained after making Speech legendary.
Edit:About that last bit. I was looking up some info regarding available choices of powers from one of the black books on Solstheim in response to a question on youtube and came to realize my character has Lover's Insight active(Do 10% more damage and get 10% better prices with the opposite sex). That explains why my prices were so much better with Thoring compared to with Seren when I still had all my perks and why my prices were still a little better with Thoring after making Speech Legendary and losing Allure. Based on that, the effect from the Allure Perk does not carry over after making Speech legendary. I can either delete that part of the answer(since it isn't really relevant anyway) or leave the full answer intact along with this paragraph.