Both really - Banks and their customers such as funds/corporates/institutions use ex. traded products heavily but also FRA's, Swaps, Depo's etc....the OTC/cash products are still big business and it's worth mentioning that where a decent, liquid listed STIR doesn't exist e.g. on en emerging market they are pretty much your only choice if you want to hedge or speculate on interest rates.
In the real world if the Money Market desk at a bank gets hit by a customer in size on an OTC instrument they'll usually try and lay it off in futures and vice-versa - bank traders will be constantly aware of the spreads between listed and OTC contracts so will pick and chose where to trade based on liquidity and rate and ensure that pricing is tight by constantly looking for arb opportunities.
