Ghostscript is a popular PostScript and PDF interpreter written in C.
I've compiled the Ghostscript 10.02.0 source code to WebAssembly and created this demo in which you can run the gs command with any arguments and it will run in the browser.
You can start by running gs -h to see the help message and check if it works.
To try out the conversion from EPS to PDF, you can run gs -sDEVICE=pdfwrite -o test.pdf test.eps. To convert from EPS to PNG, run gs -dSAFER -dBATCH -dNOPAUSE -sDEVICE=png16m -r300 -dGraphicsAlphaBits=4 -dEPSCrop -sOutputFile=test.png test.eps.