Think they are quite different and since TS is not selling Gaggia/Silvia, asking him should not help.
BZ13 is a heat exchanger
Silvia and Gaggia Classic are single boilers.
Single boiler
1. No auto boiler refill
2. Can't froth milk and brew at the same time.
3. Need to manually set the temperature for brewing coffee or produce hot steam.
4. Need to manually fill the correct amount of water in the boiler for each setting for brewing coffee or produce hot steam
5. Boiler size - Gaggia: 0.1L - Silvia: 0.35L
6. Boiler material - Gaggia: Aluminium - Silvia: Brass
7. Safety features - Gaggia: Thermostat - Silvia: Thermostat, Hi temperature limit
Heat exchanger
1. Has auto boiler refill
2. Can froth milk and brew at the same time.
3. Not necessary to set temperature or adjust the amount of water in the boiler, works out of the box.
4. Boiler size - 1.5L (BZ13)
5. Boiler material - copper
6. Safety features - BZ13: Pressurestat, low water probes, low water cut off, pressure release safety valve, thermostat, hi temperature limit
If you have most drinks done with milk, a heat exchanger is more preferred as it's easier to handle with less steps. They can froth milk and extract espresso at the same time.
Single boiler making a milk drink
HX making a milk drink
If you have to get one of the two single boilers mentioned, the Silvia will be much better than the Gaggia. The small boiler will not hold much steam for frothing milk.
BZ13 is a heat exchanger
Silvia and Gaggia Classic are single boilers.
Single boiler
1. No auto boiler refill
2. Can't froth milk and brew at the same time.
3. Need to manually set the temperature for brewing coffee or produce hot steam.
4. Need to manually fill the correct amount of water in the boiler for each setting for brewing coffee or produce hot steam
5. Boiler size - Gaggia: 0.1L - Silvia: 0.35L
6. Boiler material - Gaggia: Aluminium - Silvia: Brass
7. Safety features - Gaggia: Thermostat - Silvia: Thermostat, Hi temperature limit
Heat exchanger
1. Has auto boiler refill
2. Can froth milk and brew at the same time.
3. Not necessary to set temperature or adjust the amount of water in the boiler, works out of the box.
4. Boiler size - 1.5L (BZ13)
5. Boiler material - copper
6. Safety features - BZ13: Pressurestat, low water probes, low water cut off, pressure release safety valve, thermostat, hi temperature limit
If you have most drinks done with milk, a heat exchanger is more preferred as it's easier to handle with less steps. They can froth milk and extract espresso at the same time.
Single boiler making a milk drink
HX making a milk drink
If you have to get one of the two single boilers mentioned, the Silvia will be much better than the Gaggia. The small boiler will not hold much steam for frothing milk.