Not necessarily. But HDMI is an added feature that's always going to be welcomed because they allow phones and laptops etc to be connected too. Quality wise, it's exactly the same as DVI.
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I'd pick the BX2331 without any doubt even if it's a few hundreds expensive than the s24a300. Even though I haven't used the particular BX2331, I've used one in 21", and I've used the s24a300 and Dell ST2420L (oh wait, I was to forget that
). The BX series has colours and contrast much better than the SA300.
I've personally owned the S24A300, and the ST2420L is much better. The 21" BX series i used was well, amazing. That's just my opinion though. You might want to check the net for more.
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As for the person, I think Jshak would arguably be the best person who could help you out.