The LS9 is certainly a different beast to most of the digital mixers out there. As soon as I started mixing on the GLD, I figured that the LS9 is far more convoluted than it needs to be. The fact the LS9 is still so commonly used after all these years though, is testament to Yamaha. They are great desks even now... (even though people are beginning to shift them on now).
The thing that sets the 1608 away from the competition is it's price and aux count. Off the top of my head, only the Mixwizard gives you 6 aux sends (although I think you have to set a jumper to get them all to be prefader) at a cheaper price point. The fact that the DL1608 then has the compressors, more powerful eqs, gates, reverb, delay etc... just cements the reasons why its such a great desk. Add to the fact that it's light, compact and also allows for remote access via iPad and monitor mixes via iPad/iPhone/iPod touch... it's immense.
As for the reverb, I'm hoping that a firmware will put a better reverb in the box - I'm not hopeful though since they haven't done it since the DL1608 was released... and it has been a common complaint. It's not the end of the world but a partnership with Lexicon would be a pretty amazing addition.
From a maxing point of view, the DL32R adds More VCA and Sub mixes and an additional fx processor (as well as additional inputs and outputs obviously). The other notable features - as touched on above, is that whilst the 1608 records a show to stereo, plugging in a hard disk to the DL32R allows you to record 24 channels simultaneously (pre dsp) to disk so that you can input them into your favourite DAW and edit to your hearts content. If you reroute the USB inputs to the channels, you can play it back through the mixer - this is how you do the soundcheck without the band thing - but in reality, unless you are using a silent setup or on a massive stage where the speakers way overpower whats happening on stage, this is only partially useful as you won't get the bleed from stage. Still, great for setting up gates and tweaking eq and compressors to your hearts content. The DL32R can also be used as a 32/32 soundcard with your mac or pc. The big thing that sets the DL32R apart from the rest of the range is the inclusion of Dante - that defo puts it into at least snapping at the heals of the realms of pro audio.
The DL32R has digital gains as opposed to the rotary knobs - and a fine tune trim. It works well. Obviously, with the 1608 this is manual.
The 1608 is probably the sweet spot of the range... unless something like a DL24 comes out as for most bands, the DL32R is overkill. The other thing worth mentioning - although it hasn't happened to be an issue to me, is that the DL32R is completely wireless... whereas you do have the safety net of docking the iPad with the 1608. (Im using an Airport Extreme as my router with the DL32R).