Both have their advantages. I have both. Currently, the toolbox is stored under the deck of my house.
I previously had an aluminum cap and thought it great. It was light enough that I could put it on and take it off by myself. I now have a 'glass cap and its too heavy to handle easily by myself. To me that limits its ability to put on and take off. Also, either one is likely going to have sealant foam or something to seal between bed and cap. This can only be reused effectively so many times. I guess I would really say to not plan on taking it on and off every week.
The toolbox and the cap give you the capability to lock stuff up. How big is the stuff you want to lock up?
If you will only occasionally use the cap for camping/surfing, it might be worthwhile to get the bed tent instead.
The toolbox gives you more usable room for "truck" things but lacks security for big stuff (although you can lock stuff to it or mount it on outside of the box).
Another thought on cap. If you're getting one and have the option, certainly consider "windoors" where the side window opens like a lift gate. This avoids the issue of stuff is at the front of the bed and having to crawl in to get at it.
How big is your board? Could you lock it inside a cap? A cap also can be had with Thule racks built in for an easier mounting.
Really boils down to how you'll use it.