Some physics. Assuming the same material, length and loading, the bending strength is limited by the Second Moment of Inertia (I) of the cross sectional area. The math is complex, and even given a calculator, it's a bit confusing.
Assuming a vertical loading, You can estimate the relative change in the I value by cubing the scale change. (This estimate is accurate only for solid rectangular beams) This suggests that multiplying the vertical dimension by 1.5 would give a resulting increase in strength of 3.375 times.
If you're increasing the horizontal thickness, then you simply multiply by the scale. So increasing thickness by 1.5 would result in a strength increase of 1.5
I ran some numbers in an I calculator, and assuming a 3mm thickness, I got a value 3 times higher for 1.5" than for 1" if loaded against the longer axis, which shows that the estimator is reasonable.
For a 3mm tube of one inch, I got values of .8 and 2.75 for 1.5".
All things being equal, a hollow square is better than a hollow circle, and a hollow rectangle is better than both -- if you load it in the right direction.
Given the length and aspect ratio that you've proposed, it will be very difficult to meaningfully support the desk the long way. 16' is just way too long to get any support across. Certainly a 2x4 will be basically useless, even "on edge". Also, consider the ergonomics of having a thick tabletop surface: if this is going to be a computer workstation area you do not want to have a very thick top since that will force people to sit too low and have their keyboard too high.
I suggest ignoring the ends and building the desk to be supported the short way, i.e. cantilevered out from the wall. If you look around you will find various floating / triangle desk bracket designs. You might also consider whether adding a few legs would really be a problem; that would make the desk substantially stronger (and/or easier to build).
Whatever you do, make sure the desk is sturdy. People will invariable pile a desk with books, computer equipment, etc. and even sit on & lean against them.
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Your best bet would be the correctly sized metal screw. Not a bolt, but a screw. Some of them are self drilling/tapping (these are commonly referred to as simply "self-tapping" in the US). They will drill their own hole and tap their own threads all in one step. If you can't find the right sized metal screw, you can get a self-tapper a little bigger than the hole and it will tap itself a larger hole and hold tight. These are available at Home Depot (or any hardware store, really) in the little plastic baggies if you need a few, or in small boxes if you need a lot.
Self drilling and tapping metal screw