I used Xalan 10 years ago. I have been using Saxon almost exclusively for the last 10 years.
Not only is Saxon an XSLT 2.0 and XSLT 3.0 processor, but it is very actively developed and maintained.
Saxon 9.xx is one of the fastest XSLT processors. Its developer, Dr. Michael Kay is the Editor of the W3C XSLT WG (Working Group) and thus he is probable the one that best understands the XSLT Specification and this shows in Saxon. Any language feature is strictly and precisely implemented -- usually well ahead of other vendors.
Dr. Kay often reports the level of compliance as indicated by running the W3C XSLT and XQuery WGs test suite, which consists of tens of thousands of tests.
Saxon is supported by several IDEs, one of the most prominent being oXygen. Saxon has a very active user mailing list and the typical response time is usually measured in hours.
While I have about 11 XSLT processors installed, the one that I am using 99% of my time is Saxon.