The cleanest distinction
Postscript is a dedicated SMS choice. Omnisend is an ecommerce marketing suite.
That means Postscript is better when you already like your email stack and want to add or improve SMS. Omnisend is better when the stack itself is the problem and you want one tool to cover more of the retention work.
Where Postscript wins
Postscript wins for Shopify SMS focus. It is easier to justify when SMS has its own owner, its own goals, and its own strategy.
Where Omnisend wins
Omnisend wins when email still matters a lot. It gives you a wider set of ecommerce workflows and channels without jumping to a more expensive enterprise platform.
Where Sequenzy fits
Sequenzy fits when you looked at SMS tools but realized the next useful thing is email. If your store needs better welcome flows, cart recovery, post-purchase messages, and transactional email, Sequenzy is more direct.