[BulletproofHeart]

I think it's to do with their electronegativity but I'm not sure. I was also thinking along the lines of orbital overlap.

[SomeDude]

It is based on electronegativities.
The allen scale electronegativities of the elements are as follows.
H: 2.20
B: 2.04
Al: 1.81
For simple analysis, we can say that the greater the difference in electronegativity, the weaker the bond.
The difference in the H-B bond is only 0.16, so it is said to be covalent and strong.
The difference in the H-Al bond is 0.39, which is covalent, but not as strong as above.
Furthermore, going down and to the left on the per. table orbital size increases.  As the orbital size increases, the bond will have a lower energy and therefore will be easier to break.

Not sure what you meant by orbital overlap affecting bond strength.  H-Br and H-Al are theoretical bonds in a random theoretical molecule, so you wouldnt have to factor in orbital shape, and if you did you wouldnt be using allen scale electonegativities.

[Big-Daddy]

For simple analysis, we can say that the greater the difference in electronegativity, the weaker the bond.

That would suggest bonds between atoms of the same element would be infinitely strong and imply they were unbreakable. :p I'm interested to know the answer as well, and perhaps on an undergraduate-level forum we can go into a bit more detail?

[SomeDude]

sorry, messed that up.

when comparing bond strength of these two theoretical bonds, you can see B and Al are in the same group on the periodic table.  When youre trying to just say which one is weaker, look at the atomic orbital size.  Aluminum is larger, so it has less of a pull on its hydrogen than boron.

Also, i didnt give the right electronegativities when i listed them, but whatever, theyre close enough. 

Im an undergrad too so sorry if i was kind of vague.