Which Tank build is best really depends on two things, 1 the type of things you are doing (Raids, PvP ect) and the player behind the mouse/keyboard, after all different play styles will suite different people.
I run a Guardian Tank as my Main and have tried both Hybrid and full Defense. My opinions are based not on numbers but on my own experience which I will admit is totally subjective.
If you're still leveling or just doing Dailys and PvP at end of game then the Hybrid is a better choice as it does get both slightly improved DR and more DPS, makes Soloing stuff much easier. But if your trying to run Tank in Operations then the Full Defense Build, simple reason, Threat. In a raid the most important job a Tank has is to hold the bosses attention and keep him off the DPS and Healers and a full Defense tank has more tricks up their sleeves to help generate agro especially in the early opening phases of the fight. I don't know what the Jugg equivalents are but Guardians get both Guardian Slash and Hilt Strike from the upper half of the Defense Tree both of which generate a lot of Threat if worked into a rotation. Toth and Zorn in EC HM is a good example, when I was running Hybrid build I would keep losing agro to some of the more over-enthusiastic DPS, simply put I couldn't do damage fast enough to stay ahead on the agro table and was often faced with a choice of either allowing the boss to pound the DPS for a few seconds before the Tank Swap or use my taunts to get him back and not have them ready when the bosses jumped, you know you have an agro issue when even a Guarded DPS pulls agro twice during the first 10% of a boss fight.
After going full Defense, which tbh I did not like as much at first, I had almost no issues with hold threat, even with the same overly active DPS players, once I'd landed the first hit I could hold him no matter what the DPS threw at him. Simply open with Saber Throw, Force Leap, Hilt Smash, Guardian Slash then hit him with Force Stasis (I know it doesn't stun him but it is also a DoT) then move the boss into position and use ranged attacks (Blade Storm and Force Push) to keep agro. Very occasionally I might lose agro but then you have the AOE taunt to get it back, I no longer need to waste both taunts before the swaps occur
That being said I know at least 2 Guardian Tanks in our guild who run Hybrid spec and have few problems with agro, as I said it's more about the type of player you are, find which build you are good with and stick to it. For me it was Defense for you it might be something else.
In Flashpoints (with the possible exception on LI HM) the two builds pretty much even out..
From what you've said in your post, I think your problem is poor Focus management, which is going to gimp you at the start of a fight with the Hybrid build. With Guardian Slash more or less being equal to Overhead Slash, Hilt Strike only equaling the threat of a Sweep or Blade Storm (not to mention only useable once at the start of a fight), and Blade Storm and Overhead Slash both coming off cooldown quicker at the start than Guardian Slash and Blade Storm in a Defense build, the issue is likely that you're not understanding how to properly front load your burst threat with the hybrid, because if you do, the hybrid will actually beat full Defense in burst threat over a 30 second or so period (which is the most important part of the fight for tank threat generated by attacks rather than taunts).
Just based on what you wrote, I can tell you're inefficient with your usage of attacks, not using Sweep in your first 5 attacks makes no sense considering it puts on an important debuff and it is your best threat attack after Guardian Slash (1.3 threat modifier placed on Sweep compared to 1.5 on Guardian Slash, and it does considerably more damage than Hilt Strike).
On top of this, once you actually have the boss, the most important thing for a tank in operations is mitigation, and the hybrid wins out here.