Soundgarden is arguably the best band of the last thirty years due to their music being similar in composition to classical music, though lacking in it's technicality on guitars, the heart is still apparent in the way that minimal notes are used in a variety of fashions. The drumming is by far the best since John Bonham, both having similarity in precise rhythm and powerful strikes. The vocals are superb and great for learning to slide in and out of octaves smoothly while gaining a mid-range. Chris Cornell as a songwriter collects from many different eras and his lyrics are relative to most anyone as well as beautiful. The band itself is a modern day Beatles in their knack for having on any album, at least 1/4 of the songs written by each member individually, each member is an excellent songwriter.
I've never been a big fan of Soundgarden. Don't get me wrong, they aren't bad, they always sounded good, but their songwriting lacked. I'm not a music buff, but of the bands I care for I'd go with Metallica, Fleetwood Mac (do they count? Sure their best work was behind them in '83, but they were [are?] still around. Even a little more recently, Alice in Chains (with Staley) and Godsmack are better than Soundgarden ever was.
Obviously this is open to individual preferences, but I find it to be rather closed minded to single out one band as the "best". While I agree that soundgarden is a decent band, there have been various other bands equally good, if not better. You are also discounting the diverse immensity of musical genres that exist. Such as ambient techno: Aphex Twin, Locust Toybox, Boards of Canada, etc. Psychedelic rock: Tame Impala, MGMT, Flaming Lips, etc. Also, so many other nineties grunge bands like Nirvana, Alice in Chains, and Pearl Jam.
From a musicians standpoint i would say pearl jam. I can learn a full soundgarden song on guitar in around 25 minutes, this is to where i can play it perfectly with the record. Pearl jam even flow took me about 2 hours because of the complexity in their songwriting. I believe Pearl jam consists of the more talented members
Pink Floyd, the Final Cut, 1983. If that qualifies them as a :band of the last 30 years" the answer to this is no.
[Now I find myself once again trying to fill 50 words to hit the minimum because the first 5 were all that needed to be said on this issue]