There are grown men who buy legos and play with them
What I did was bought one of those giant double wide, shallow, under the bed plastic sweater bins. It holds everything, slides out of sight and is easy to access. The kids pull it out when they want to play and slide it back when they are done.
Since it is shallow and clear, they don't pull as many legos out at a time as they did with the deeper storage bins.
FYI, I have boys just a little older than yours, and what I ended up doing was to box up or get rid of just about every other toy but the legos. That helped a ton with getting rid of the mess. The only other indoor toys they play with now and then are their Bakugans and Transformers, but those mostly stay put away in bins. Legos are the only toys they play with daily.