Adjustable Grip Hitch
First the differences: While these two hitches look very similar, they have very different structure. While the structure of the Rolling Hitch (AKA Taughtline, Midshipman's, Tent-line etc) is considered a base hitch (many other variants are based on the Rolling Hitch) the Adjustable Grip Hitch is, I think related but, not a variant.
The Adjustable Grip Hitch is more similar to the Blake's Hitch in the way it is tied.
Both hitches 'grab' the same way. The Rolling Hitch and the Adjustable grip Hitch 'pin' the hitch to the load bearing line by way af a smart lever. Both can improved on slippery rope by adding turns, thereby increasing the mechanical advantage of the lever. Because if this structure, the harder the pull, the more they grab.
Both are very easy to tie and to learn to tie. I have tied the Adjustable Grip Hitch a few hundred times by now (compared to maybe tens of thousands for the Taughtline Hitch) and I can tie both with almost equal speed. I can still tie the Taughtline faster, but I think that is due to many years of using it; with time I am sure I could tie the Adjustable Grip Hitch as fast.
After three nights and three days there has been no noticable difference in either hitch on the testing tarp. Both have held well. I retied them last night as slipped hitches to see which one was better tied this way or if it effected the gripping power of either one. Again, there is no noticeable difference. Both hitches tied up easily as slips and held well in the Mason Line I was using to test. As of this morning, there have been no failures by either hitch when tied in either configuration.
Tieing up: One of the things I like about the Rolling Hitch is as soon as the second turn is 'tucked up' the line takes all of the load; you no longer have to hold the load. This makes it easy to finish the other turns with both hands free, especially helpful in very winds conditions (when tieing a tarp) or when you are securing a very heavy load. After the second turn you don't need to 'pull' the cord anymore, the Rolling Hitch has it, the Adjustable Grip Hitch doesn't. Because the Adjustable Grip Hitch doesn't bear the load until the final turn/hitch, you must hold the load until the hitch is fully dressed. Dressing the Adjustable Grip Hitch is also slightly more difficult in stiff, sheathed synthetics. Because the first turns have no load you must dress them individually before the load can be relesed. While this isn't a concern on slack practice rope, it could be in real world situations, just something to consider.
Both hitches seem to hold very well. Each can have improved gripping power by adding turns.
Both hitches are easy to learn.
Both hitches can easily be tied as slipped hitches and not degrade the gripping power.
The Rolling Hitch wins on Tie up, being able to take the load sooner than the Adjustable Grip Hitch.
The Rolling Hitch wins on stiff cord needing less dressing than the Adjustable Grip Hitch; and what it does need is easy to perform due to the fact that all the dressing it needs can be performed after the hitch has taken the load. The adjustable Grip Hitch must be dressed with one hand, while the other holds the load.
All things considered: The Rolling Hitch (Taughtline Hitch) is still the winner due to taking the load sooner and less dressing needed. Otherwise both hitches are good performers.