There are three key differences.
1) Greater Range of Sparkling Beverages: You can sparkle almost any liquid (e.g., water, fruit infusions, tea, mimosas, etc.) in your Spärkel whereas you may only carbonate water with a Sodastream. As a result, the range of sparkling beverages you can create with a Spärkel is broader than with a Sodastream.
2) Convenient Carbonators: Sodastream uses a high pressure compressed gas jetted from a CO2 tank to carbonate. Spärkel uses small sachets of citric acid and sodium bicarbonate to carbonate. As a result, Spärkel carbonators can be conveniently delivered to your door and there is no empty tank to return. In addition, you will not unexpectedly run out of Spärkel carbonators since you see exactly how many are remaining. With a CO2 tank, the quantity of CO2 remaining in the tank is hard to know since there is typically not a gas gauge included with home carbonation systems.
3) Carbonation Consistency: Each Spärkel carbonator generates the exact same amount of CO2 gas. A consistent level of carbonation is easily determined by touching a button indicating Level 1, 2, 3, 4 or 5 (where 1 is least bubbly and 5 is most bubbly). Therefore, consistent carbonation is conveniently possible for a given beverage type at a given beverage temperature. In contrast, with most home carbonation systems, the amount of CO2 that is jetted depends upon how full the tank is and for most models, how long/many times the user jets the CO2. When the CO2 tank is very full, the pressure is high and more CO2 is jetted. As the tank empties, the pressure declines and less CO2 is jetted. Carbonation consistency will vary based on how full the CO2 tank is and depending upon how the user manually operates the system.