if compared to the fatboy tubes, which is most effective at slowing the shorty barrel cycle rate?

They are probably about equal, the pigtail is a bad product, they are bent tubes and cryogenically stress relieved, meaning if you dump 3-4 30rd mags they will try to straighten, because they get too hot for the cryogenic treatment to hold out.  Good product for law enforcement officers and semi auto users who will never dump 3-4 mags, bad product for military personell or heavy recreational users.

The Fatboy won't burn out, but depending on your barrel's gas port it might not function properly installed either (if not enough gas gets to the BC it will short stroke, the barrels that are perfect for these are 10.5's with a couple thousand rounds through them, or 10.5's by companies like model1sales that allready have huge gas ports. As a general rule if your 10.5's kick is very spikey and rate of fire around 900-1200rpm the fatboy gas tube will be perfect. (A brand new barrel with a small gas port might not cycle).

i have a newish 11.5" bushy semi auto and it does have a pretty harsh recoil i assume from the gas spike. thanks for the tip.

No problem, I had a model 1 Sales 11.5 and it had really harsh recoil and I wondered if I was imagining it or being a pussy. I fired it in auto and ROF was over 1000RPM.  Yeah- obviously it was getting WAY too much gas.

The Pri tube will bring that down to about 750rpm.

My new LMT has the Sopmod II LMT B/BC (really designed for M4's not the 10.5). Anyway it has a ROF of around 500rpm (It is almost funny slow.) Good though, with a KAC sound suppressor installed ROF should be around 650-750RPM. Recoil is very light.