Where the primary focus of ECLiPSe is constraint handling, this is not the case for SWI-Prolog. Some of the constraint libraries such as CHR and clp(qr) have a single origin and have been ported to several systems. You can expect similar behavior and performance, though some have evolved further on some systems.
Systems that entered the constraint domain early typically implemented the finite domain solver in low-level code. SWI-Prolog’s is the work of Markus Triska and is a pure Prolog implementation. In many cases it will be a lot slower than ECLiPSe. It also comes with some advantages, such as support for unbounded integers.
I guess you need concrete experiments to figure out whether SWI-Prolog’s constraint handling is “good emough” for you. If you do not depend too much on SWI-Prolog’s extensions that are not supported by ECLiPSE, switching at some point should not be too hard. Given time and money, SWI-Prolog’s constraint handling can also be improved 