I have a FoodSaver (home-use vacuum sealer) and a commercial vacuum sealer. I assume the hand pump one you mean is this. I have the predecessor of that one, which is a hand-held sealer with batteries. Yeah, I like to seal things 
The pros/cons:
Hand-held: It’s cheap. It also takes special ziploc bags, which are more expensive than normal ziplocs (list price for 12 quart-size bags is $4.29, working out to about 36 cents each). The mechanism is fiddly; you can’t fill the bags all the way up, because the plastic dimple you attach the pump to is in the upper right corner, and to get a good seal you need that to be on a flat surface. It can be kind of tricky to get it to seal, but if you do get it sealed, it works.
The other big advantage of this system is it’s the only one that you can open the bag and then re-seal it without much hassle.
FoodSaver: as others have said, this works pretty well. The bags can be pricy (list price $11.99 for 20 quart-size bags, or about 60 cents each). You can bring that down a little by buying rolls of bag-plastic and sealing your own, but it still ain’t cheap. I’ve had trouble getting good seals with these at times. You can’t easily seal liquids in them (the vacuum pulls it out).
A big advantage of this system is that you’re only limited by the size of the bag. If you buy the rolls of plastic, you can make pretty long bags.
Commercial (“Chamber”) sealer: I only have experience with one of the smaller versions of these. Two big drawbacks: they’re expensive (large ones can be thousands of dollars) and they’re big & heavy. You don’t buy one of these and stuff 'em in a cupboard and only pull them out when you need them. The one I linked weighs 50 pounds; it lives on the counter.
Advantages: The bags are cheap - 500 6x12" bags, which hold slightly less than a quart, retail for 49.95. That’s 9 cents each, and if you buy from a discounter or in larger quantities you can get that down to 2 or 3 cents a bag. The machine and sealing process itself is much more hands-off than the other two methods, and more reliable. I get less leakage with this machine than the other two by far.
You can also seal liquids in it, no problem. The vacuum is powerful enough that you can use it to force marinades into food - I’ve infused fruit with flavorings and liquors, for example (watermelon infused with Tequila and Chile powder makes a great appetizer). It’s also a TON of fun to watch as it pumps all the air out of the chamber before sealing.
Disadvantages: As I mentioned above, the price, and the size/weight. This is not for the faint of heart. The size of what you seal is limited by the size of the chamber.
I will say this: Now that I have the chamber sealer, and I have room for it to sit on my counter, I use it ALL THE TIME. It’s really convenient, and I never feel bad about throwing stuff in a vacuum bag because the bags are so cheap. I wasn’t sure when I bought it if I’d use it enough to make it worth the money, but I’ve had it for a year now, and it’s one of my favorite kitchen gadgets.