SSR vs optocoupler with TRIAC output
There are enough interesting things that haven't been said that another answer may be useful.
As well as adding new material this will overlap various others for better overall completeness.
TRIAC is an AC switch except in a special case.
Turnon occurs when opto is driven above enable level. If opto is turned off and TRIAC load current is above holding current the TRIAC will remain on until the next zero crossing of the load signal.
If opto is left on the TRIAC will refire at subsequent zero crossings until the opto is turned off.
Holding Current: If the load current is below the minimum "holding current" the TRIAC will turn off as soon as the opto is turned off. Here (page 5) the holding current is 25 mA max. If load current is above 25 mA the TRIAc will hold on until the next zero crossing if opto is turned off. Because they have been sloppy and have not specified min or typ values for holding current all you can say about currents below 25 mA is that the TRIAC may stay on when the opto is turned off. This parameter can be of significant importance when light loads are being switched.
At say 5mA you may think that the TRIAC is a zero crossing switch, but it may not be. Or at 10 mA. If you are switching eg an inductive load at 230 VAC or about 300 Vpeak, the load power is about 3 Watts instantaneous at Vpeak. If the opto is turned off at Vpeak with an inductive load then an appreciable amount of energy may need to be dissipated or controlled. In such cases snubber design may need to be considered despite the zero crossing aspects.
The FET SSR has 2 x FETs connected "back to back" for AC. For DC the two FETs can be connected in parallel, doubling the current rating from 1 A to 2A.
The TRIAC SSR switches in 100 ns max. The FET SSR is about 5 x slower and assymetric on operate and release.
The TRIAC SSR has a 5 mA / 10 mA max LED requirement (2 grades). In their example circuit they drive it at double this value. The FET SSR has a max 2 mA turn on , 0.5 mA typical and 50 uA min turn off current !!!.
Importantly, as opto current is reduced a TRIAC SSR may "just stop firing". A FET SSR will tend to degrade gracefully. Note though that low FET drive MAY lead to higher than intended IC dissipation.
The TRIAC SSR specifies a 100 V/uS min rate of off state output voltage rise. At rise times above this the TRIAC may decide to turn on "all by itself". "This can be embarrassing".
The FET SSR tends not to have this limit - but hitting the output with too fast a risetime is 'probably not wise'. The TRIAC will stay on once turned on. IF one managed to turn on the FET it would probably turn off again shortly thereafter. This may or may not be a good thing.
More anon maybe ...
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The SSR is a low voltage DC device, but may also be used for low voltage AC, while the triac device is for AC usage only, typically mains voltage.
A triac has a PNPN-structure, which means that there will always be a voltage drop across it, while FETs are resistive devices, and for those an \$R_{ON}\$ is specified, in this case 0.25\$\Omega\$ maximum.
The voltage drop over the triac makes opto-triacs less convenient for low voltages, where they may drop out too much of the available voltage. For instance a 3V drop on a 24V supply means that you lose 13%. So it looks like in your case the "SSR" is a better choice. You'll have to look at the maximum current, though. The datasheet says 2A, but on the Absolute Maximum Ratings graph it shows 1A. My guess is that this should be read as a normalized value, and that the actual maximum is indeed 2A, to be derated at higher temperatures.
TRIACs and SCRs have a significant on voltage, a bit over one diode drop. MOSFETs can turn on such that the voltage drop accross them is much less. On the flip side, the control and driving circuitry will be more complicated.
For low voltage applications, the voltage drop can be significant. For high voltage applications the few 100 mV accross the SCR or TRIAC is a small fraction of the total and therefore doesn't matter much. The simpler drive and higher voltage tolerance of the bipolar versus FET makeup then becomes advantageous.