A saxophone gig bag is an alternative to a hard case that is easier to transport to and from home, rehearsals, or performances. A gig bag is often lighter than an instrument case, and they tend to have shoulder straps, are available in backpack styles, and can have roller wheels to make it easier for you to get around with your instrument.
Safety first is the most important thing to remember when thinking about transporting your prized instruments all over the place. A traditional wood case has a hard shell and form fit inside. The safest place for your sax is in a hard case. But, even a hard case will not protect your sax from all types of damage.
Younger sax players might think they can sit on their case or might even toss it in the car or into their room. I have seen body damage both on saxophones in hard cases and on saxophones in gig bags. These sax case issues are mostly perception and user error when a sax is damaged in a case or gig bag.
We have to realize that no case offers 100% protection for any saxophone. I have seen saxophones that were run over by trucks. Honestly, the sax did not have a chance, and it didn't matter whether the sax was in a case or gig bag. A case or bag offers more protection than a paper bag, but nothing will protect your saxophone from a large 4-wheel drive. We have to remember that a bag or case helps protect a sax, but will never replace a caring and cautious student of the saxophone. You have to be careful with your saxophones!
My favorite saxophone cases and gig bags are going to be hard cases that don't give. The Gator ABS cases, Walt Johnson, and J. Winter flight cases are favorites. Hard cases that better protect a sax require less concern over possible damage than soft bags. The disadvantage to these cases is accessory storage space. They offer very little room for accessories, with the exception of your primary mouthpiece, reeds and strap.
In the traditional gig bag area, the inside foam padding becomes a larger part of the protection to the saxophone. The Gator GL series gig bag and Protec Contoured Pro Pac saxophone gig bag are good options but there are many manufacturers creating good bags for the sax today.
The primary things to look for are the padding inside the case and the quality of the zipper and straps. A great bag that you can't close is useless. A great bag that the zipper pops open on is dangerous and a dust protector with no inside padded protection is a ticking time bomb.
I would seriously reconsider getting a gig bag-style case for a younger student that might struggle to be careful. You are asking for ongoing repair bills each time the bag gets tripped on or tossed in the car carelessly. The Giardinelli Premium Lightweight Saxophone Case or Pro Tec MAX Rectangular Sax Case are good examples of a modern-style replacement case that offers solid protection with the added bonus of shoulder straps for transport with added pockets for saxophone accessories.
The best formula for considering case and gig bag options is to look first at the instrument cost and then consider the primary handler of that instrument. A responsible choice for both is a smart purchase for all. And please remember that the best protection for any musical instrument is proper care when handling and transporting your instrument. It is your saxophone. Treat it with respect and keep it safe!