Now I'm gonna butt heads with you regards to the Alpina roadsters wheels. I just don't like the style Alpina went with in regards to that style of wheel. Now, the Alpina "classics" wheels are where it's at. Before I had my C2, I owned an E30 325i with a Tech 2 body kit and I put a set of genuine staggered Alpina wheels on it, as they just look amazing.
I actually want to get a set of classic style Alpina wheels to go on my M. On the Z4 forum, this got a bit of a negative response from other forum users, as they believe that you should have either M wheels or the CSL's. Sadly it seems the Alpina classic's that were done for the Z4 are NLA and I've been struggling to narrow down any website etc where I can get a NOS or mint condition examples.
With regards to the M looking too much like a normal Z4, I think that's not wrong, but not exactly right either. I would argue that bar the interior on the Alpina, they are just as much subtle differences with it, as there is with an M. But it's these subtle differences which is classically the ethos of both BMW tuning houses. It's not really until the mid/late 2000's that BMW did massive differences cosmetically with their M cars (bar the E30 M3). Let's face facts (yes I said facts), if you asked a non-petrolhead to pick out the different Z4 from a lineup with an Alpina, M and 3.0 , they would say they are all the same car. It's only really BMW/Z4 fans that would notice the difference in the first place.
I can't comment about the sound, as I've never heard an Alpina in the flesh and it's foolish to go by how they sound on YouTune, due to the compression they use really screwing with the tone heard on the audio. From my own experiences of dealing with Alpina's, they do typically have a more bassy/rumble edge to them when compared to a standard BMW from the same model line. After the shitstorm my Impreza P1 caused when it had a Blitz NUR spec 3.5" exhaust with one of my neighbours, I was really hyper-aware about not disturbing them after it took several years for them to become civil again. Add in the fact they now have two young kids, I didn't want to be coming home late at night and wake them up, as it's not fair on them. Now my dads E46 M3 had an aftermarket stainless system on it and it really made it more boomy/bassy , but I actually didn't like it too much.
Living in Oxford, where there is not much love when it comes to cars and just how viscous the city council are towards motorists, I did not want to draw unwanted attention to myself and end up with fines left, right and centre to deal with.
I think you were on the money about the Alpina being a GT car. That's what any Alpina is. They are a more refined and quicker version of the normal production line, where an M car is a more raw and quicker version. While both cars are Z4's , they are not built to do the same job or really compete with each other. Personally, I think the Alpina would handle better on B-Roads, due to it most likely having a softer spring and dampening setting, which can cope with the rough road surfaces most commonly found with B-Roads and even more so with Oxford's roads. When out in my M, I have found the back end wants to skip on bumpy sections frequently as they are too stiff. My Impreza P1 which was designed and built by Prodrive, with the specific goal of being a B-Road slayer, had much softer settings than the JDM Impreza STi Type-R (these are the top of the range 2 door Impreza's from the mid to late 90's).
In the days when I owned E30's, there was a common saying on the forums I used, known as "M Tax". Which boiled down to any M part, be it for the M3 or just the M-Sport options, would typically be around 20-30% more than standard parts. However, Alpina take this to a whole different level. I remember I needed to get a new downpipe for my C2 and Alpina quoted me £1200 and a 4 month wait to get the part, even though I could install an OEM 325i version for about £700 and aftermarket was even cheaper still!
I think it's a fool errands to make a statement that one version is better than the other, as they are just not built to do the same thing or are they built at the same audience. When I was looking at what car to get, it didn't matter to me one way or the other which version I went for, as for me, my car is about rebuilding a life after it all started to unravel when I suffered serious and life changing spinal injuries, which deteriorated to the point where I was unable to drive for a number of years and became a recluse, as I had nothing to go out for. So no matter which version I went for, the ultimate goal was to rebuild my social life and get out of the house, while gaining some sense of independence.
Do I like the Alpina? Yes, but I also liked the M the same amount and it just made more sense to choose it over one of the two Alpina roadsters that were up for sale and were in my price range back in November last year. Do I envy the Alpina? Not really but if I had gotten an Alpina, I would pretty much feel the same way towards the M. Also, in your case, you already had an M car with your Z3, so it totally makes more sense for you to have the Alpina, as I bet owning two raw roadsters would have felt like a waste of money?
Also I'll agree ref the LSD, the difference in grip between my Z3M and the Alpina is night and day, that said the Alpina feels more like a GT than a sports car, the M is just a hooligan and behaves like one, but the grip is amazing, but you can turn it off and start praying 
