Here is how I see things on this;
First, you need to divide the AT in two group, the AT guns and the TDs.
The AT guns are slow, and need a truck to be able to move in the offense, and hence are very vulnerable when in their trucks. However they do dig in quite well, and can have a good entrenchment value. They are however still very easily destroyed by infantry, but against armoured vehicles they are real killers.
Pro - very good against armour, digs in well
Con - weak against infantry, slow moving and needs transports.
The TDs are basically turretless tanks. They move well, work well against armour, defend VERY well against armour, and as already mentioned, are cheaper than the equivalent tanks. They do however not dig in very well, and in rough terrain (hills, cities, forests, swamps etc) they are very exposed to infantry attacks. The higher TDs, are however well suited to attack infantry in the open, but they cannot defend against them.
Pro - good speed, good against armour, higher levels can attack infantry in the open
Con - are very vulnerable in rough terrain, vulnerable to aircrafts.
All this being said, I tend to buy (I've not bought Allied commander as I enjoy playing the underdog) 1 PzJg1 rather early, and another quickly thereafter. In the first two years I do not use them very actively, but allow them to gain experience by killing off weakened non entrenched units. When you are able to get the Marders and StuGs, things change. For one, they are really effective at killing of fortresses/strongpoints, and they can be quite lethal against tanks. I never upgrade to the Ferdinand/Elephant, as it is too slow. When the JagdPanther arrives however, I go straight for it. This to me is the pinnacle of the TD design. It is fast, it can attack infantry well, and it is lethal to enemy tanks. The upgrade to JagdTiger is NOT a good idea imo, as it is slower. In my last -45 Seelowe, my mobile force consisted of 4xMaus, 4xPanther, 3xKingTiger and 6xJagdPanther. The trick with the JagdPanther is to make sure it is only attacked by enemy armoured units, and not leave it in vulnerable positions.
As to TDs vs Tanks. The tanks are usually more versatile, that is true, but the TDs tend to be better tank killers, and as mentioned, they are cheaper, something that makes a difference in the higher difficulties. However you will not succeed with nothing but TDs, as they will be chewed up by enemy infantry if left in the wrong positions. As I see it, the tanks are split in two, the heavies and the mediums. The Heavies for me usually follows a line like this;
PzIV - >Tiger -> KingTiger -> Maus
The medium line is;
PzIII -> Panther
I will usually use the heavies to breech the enemy line, use the mediums to strike deeper into the enemy line, and allow the TDs to mop up what remains of the enemy line.
"Hun skal torpederes!" - Birger Eriksen
("She is to be torpedoed!")