Since this question of which is the fastest to reload (box or tube) is obviously of vital national importance, I felt it was my duty to conduct an experiment to satisfy my curiosity.
I used a Remington Speedmaster and a Ruger 10/22.
I figured that starting from pulling the trigger in a standing position would give me the most consistent results. Since I don't have a range handy at the moment, I used the following procedure while my wife was out at the grocery.
1) Set stopwatch to zero.
2) Verify rifle is empty.
3) Verify rifle is empty again.
4) Verify rifle is empty again.
5) Hold rifle in shooting position to shoulder with weak hand in normal position on forestock.
6) Start stopwatch (iphone) with trigger finger.
7) Grasp stock and pull trigger
8A) Tube: Flip rifle over in weak hand and extend tube with strong hand
8B) Box Mag: Shift gun to crook of weak arm while dropping mag into weak hand.
9) Both: Grab a handful of .22's from open Federal bulk box with strong hand.
10A) Tube: Drop 10 cartridges into tube mag.
10B) Box Mag: Insert 10 cartridges into Box mag.
Note: This step took the longest and about equal time in both cases. You must manipulate the cartridges in your hand into the rim-first position required for both types of magazines. I found that it took me as long to line the rim up with the rim-slot in the tube and drop the cartridge as it did to stick them in the magazine.
11A) Tube: Slide tube in and lock in place with strong hand.
11B) Box Mag: Grab stock with strong hand in trigger position while inserting magazine into gun with weak hand.
12) Lift gun into firing position and pull trigger. Look at stopwatch.
Note that I did not cycle the bolt to load a round or cock the gun prior to step 12. I did not want to shoot up my milling machine which I was using as a backstop.
11) Unload gun and repeat from step 1.
RESULTS:
I did it 5 times for each gun. Both guns averaged around 25 seconds. Fastest was 23 for both guns, slowest was 28 for both guns. Biggest factor for both guns was how many of the cartridges in my hand had to be flipped around to get the rim into the correct position. A couple of times I dropped 2 or 3 cartridges so I made sure to always grab a few more than 10.
CONCLUSION:
There is no significant difference in how fast you can reload and fire a .22 again with a tube magazine or a single box magazine.