Both strategies protect the eggs (e.g. from infanticide, as female water bugs are known to destroy the egg clutches of other females) and help them survive by keeping them moist and oxygenated. Back brooders tend to keep near the surface, sometimes surfacing where oxygen is more available. Other times they do "push-ups" underwater, which keeps fresher water flowing over the eggs.
Lethocerinae eggs are laid above the surface, meaning they have plenty of oxygen but are in danger of drying out. The male prevents this by climbing up to the eggs (he keeps an eye on them from underwater) and lets water drip off him onto his offspring. In some species, males regurgitate water onto the eggs.
Because of all this effort - it takes between 1 and 3 weeks of this care for the eggs to hatch - males want to be sure the eggs are theirs. But the females can store sperm from previous encounters, which is a not a good thing for males. So the male insists they mate maybe 3 times (at least), then he'll let her lay some eggs. Then they'll mate another few times, and she can lay a few more. It's not unknown for them to have sex 50 times before the male is satisfied, taking perhaps six hours. All these matings make it unlikely any of the eggs will be sired by another male, as anyone else's sperm will struggle to fertilize eggs when there's so much of his.
Sometimes though, you've got to look after Number One. When food is scarce males may eat the eggs of other water bugs, sometimes even their own. This also occurs when something has gone wrong with the eggs, such as faulty development, and the male cuts his losses and tries to get some of the energy he's invested back.
Photo: Left - Water bug (genus: Lethocerus) guarding its eggs (credit to Hyla 2009). Right - Water bug (genus: Abedus) carrying its eggs on its back (credit to Greg Mayberry).
Sources and further reading:
Alcock, J. (2009). Animal Behaviour. Massachusetts: Sinauer Associates.