Seems to be some confusion here.
"Chop Saw" generally refers to an abrasive cut off saw. Most use 14" abrasive blades running high RPM's (3500RPM+) and are the cheapest option. Downside is the heat, sparks, accuracy and cleanliness of the cut. They really suck for doing mitre cuts fast and your capacity is limited by the blade wear. The advantage to the chop saw is low cost, cut's fairly quick and most importantly any mouth breather can run one. No worries about your neighbor coming over to use it and ruining an expensive blade.
Dry Cut Saw looks like a chop saw but beefier. They run much lower RPM's (1000-1800) and use more expensive carbide tipped blades. These cost more than a chop saw but are less expensive than a GOOD bandsaw or cold cut saw. Dry Cut saw cuts much like a bandsaw, cool, clean, and accurate. Downside is they are still a bit loud and throw chips everywhere. They also are still not the quickest to reposition for various cutting angles. They also share the same downside as the abrasive saw in that you have to do the actual cutting which takes time and wears you out. The blades are expensive if somebody doesn't know what they are doing and wrecks one.
Cold Cut Saws are supposed to be very low speed (less than 100rpm), high torque, beefy saws with coolant systems and HSS blades. Many interchange cold cut and dry cut. Cold cut saws are expensive and have the coolant mess, however the coolant mess may be okay with some since you dont have the spark or chip mess like with the dry cut and abrasive saws. Many also come with downfeed options if you wish which saws you time and energy.
Bandsaws come in many shapes and sizes obviously and are what the name implies, a bandsaw. Horizontal saws like the Ellis are popular, as are other cheaper versions like the Jet. Vertical saws can either be the smaller ones used for light intricate stuff, or the huge coolant fed ones you see in heavier fab shops. Obviously there are many variations available, so simply stating a bandsaw is best without refrencing the type means very little. Bandsaws disadvantages are their costs, the space they take up, the slight mental capacity they require to operate and the fact that most are not portable and if they are, you wont be doing much but moving it around the shop. Advantages are the low noise level, very little mess (filings just fall into a pan or on ground, nothing flying), clean cool accurate cuts, many have downfeed controls so you set it and walk away and depending on the model, fast setup for mitre's. Many have a very large capacity as well.
Personally I like the Ellis style saws the most for most general fab work. Quick and easy to use, downfeed control saves you time and energy, easy to service and overall a decent bang for the buck. If you go that route I strongly suggest gong with a 1600 or better as the 1"+ blade machines are much better overall. The cost is high though, look around craiglist and you can score some deals.
