The main difference is chemical composition. Both alloys are allowed within ISO 15156, although there are restrictions. In general, 718 would be considered more suitable.
The restrictions are critical, they deal with environmental factors and suitable heat treatments.
Neither alloy has outstanding corrosion resistance, but they are fairly good and they do have high strength.
The only alloy that would generally be considered to have similar strength and better corrosion resistance would be MP35N.
Alloy 718 more suited for this kind of service because of the presence of Mo into its chemistry. Though alloy X-750 can withstand this service, it is the lack of Mo in alloy X-750 that makes it more susceptible to intergranular stress corrosion cracking. The specially limited chemistry version of alloy 718 offers adequate resistance within the lower H2S concentration range, where the carbon content is limited to 0.03% and trace amounts of other elements are included to fight against IGSCC. For higher H2S concentrations and temperatures, alloy 725 will offer superior results, though if it's feasible for your budget, alloy MP35N as stated by Ed will undoubtedly offer the best performance.
It depends entirely upon application which alloy is better. NACE MR0175 allows X750 up to 50HRC for springs, whereas alloy 718 is never allowed above 40HRC in sour service. If you have a spring needing the highest strength and fatigue life, X750 may be better. As others have stated, 718 will have better corrosion resistance in general. Environmentally assisted fatigue may need to be compared between the two in your fluid for a spring application.
Just always remember, NACE sour service requirements only pertain to cracking in H2S containing fluids. They don't take into account corrosion, fatigue life, stress requirements, etc. for a part. These concerns need to be considered separately.