This is an interesting thread. I have two Stradic 2500s, a Daiwa 'Advantage' in 2508 size I think, and two Daiwa TDR 3012s. I also have a Mitchell 300A of 1978 vintage. I have vague memories of an Intrepid Black Prince, but thankfully they have faded over the years.
Predictably, the Mitchell is still going strong, with nothing ever replaced except the line on the spools (but serviced by myself). It has hardly been hammered, but is the most enduring item of tackle I have by a considerable margin. It may not be the flavour of the day any more, but for float anglers in particular, it had (has still) features important to this style of fishing - doubly so if you fish running water; these include:
A sensibly-sized spool
Good line lay (certainly for the time)
A spool which can easily be reached
For the matchmen (of the time - much more legering - and pole fishing - done these days) and general float angler, these features outweighed the disadvantages. This even applied to right-handers fishing with a rotor direction which seemed to favour left-handers. As Alan Tyler said, the current choice of reels favours right-handers. However, I can recall being shown by some very able exponents of the Mitchell Match how to overcome the problem of picking the line up cleanly at the end of a trot; the use of tiny barbless hooks meant that this was a skill which needed plenty of practise, especially for matches! I was also shown a couple of ways of closing the bail arm manually. Many older Trent anglers still favour the Mitchell. It still has a lot to offer if you are prepared or able to negotiate the significant shortcomings.
I agree with some posts about modern (recent) reels being 'better' than the Mitchells, but I can only comment on the reels I have owned. What remains to be proven is the reliability and robustness of the Shimanos and Daiwas I also own. Irrespective of a smoother operation, I have reservatins about the longevity of the newer reels. I think that one of the reasons Mitchells retained their popularity for so long was that the more modern alternatives have only very recently combined all the genuinely useful advantages together ;for me these are - for float reels in particular - excellent line lay, a spool lip within easy reach (which means you can hold the rod properly), smoothness, and that essential quality which means you don't have to constantly think about the operation of the reel. Older alternatives, which have included Shimano and Daiwa, oflen had a 'coned' spool which put the lip out of easy reach of the (ideally in my opinion) index finger (rather than middle finger). Part of the problem is that float anglers who fish running water are a fraction of the whole market. I think (but I could be wrong!) most are produced for a 'spinning' market.
Mark Wintle did some excellent articles about the ideal fixed spool reel for trotting. He obviously knows what he is talking about (how about some more articles, Mark?). I would post a link, but should admit that I am probably better at fishing than IT!
So...for me it's Shimano Stradic 2500FA and 2500FB for all float fishing, Daiwa Advantage for 'medium' river feeder fishing, and the TDR 3012s for heavy/long chuck feedering. There are almost certainly other reels which fit the bill, but I have no practical experience of them. I have no doubt that the Mitcell would still catch me plenty of fish, but I have semi-retired the old girl, and limit her use to swingtipping with a glass rod - something which I think is more in keeping with her place in history.