The verdict
For most online stores I would pick Omnisend. You can start on a free plan, you get email, SMS and push together, and you are not tied to one shop platform. If your brand is on Shopify and you want SMS to carry serious revenue, with opt-in tools and compliance help built around it, pick Postscript.
Check the cost shape before you decide. Omnisend plans scale with your contact count and SMS is billed per message. Postscript charges per message with carrier fees as a separate line, so costs follow your sending. Model a normal month and a peak month in either tool.