Dear Memphis, I have used HDS under Linux for some thing near 1 year. The difference? There is no difference except that you are running linux, an open source operating system, with much more capabilities than it's competitors.
OH! Really you want me to compare that toy with HDL Designer!! Active-HDL is I think only for those persons who want to begin the VLSI design and do not know any thing and do not have any experience about big project. Leave the toy away. Use HDS, when linked with modelsim or NC-Sim, it is much more powerful than AHDL.